Jan CamenischIBM Research ndash Zurich

Joint work with Ernie Brickell Liqun Chen Manu Drivers Anja Lehmann

jcazurichibmcom JanCamenisch ibmbizjancamenisch

Direct Anonymous AttestationRevisited

Direct Anonymous Attestation ndash What is it

Protocol standardized by TCG (trusted computing group) Attestation of computer state by TPM (root of trust) TPM measures boot sequence TPM attest boot sequence to third party Attestation based on cryptographic keys

rarr Strong authentication of TPM with privacy

Use cases apart from attestation secure access to networks services any resources of devices can be extended to user of device

Irsquom TPM123 and host runs software xyz

Direct Anonymous Attestation ndash Brief History TCPA 044 ndash July 2000 until TCPA 11b ndash February 2002

wout DAA but used Privacy CA Privacy groups criticized Privacy CA solution

TPM 12 ndash July 2003 until Aug 2009 (revision 116) DAA introduced as alternative to Privacy CA goal to make privacy groups happy DAA based on RSA Host part specified in TSS (Trusted Software Stack) Implementation on chips very slow (arithmetic co-processor)

TPM 20 ndash October 2014 Elliptic curve-based DAA ISO standard in 2015 (ISOIEC 11889)

Today Interest in TPM revived Security of mobile devices FIDO authentication

Attestation Scenario

Issuer

(TPM or Platform Manufacturer)

Verifier

(Bank eShop Tax authority hellip)

Problem using traditional certificates all transactions of the same platform become linkable -(

JOIN

SIGN

Privacy barrier

Security Requirements for Attestation

Unforgeability No adversary can create signatures on messages that were never signed by a certified TPMAnonymity signatures by an honest platform are unlinkable (without basename or different basenames)Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this messageRevocation If a TPM is compromised signatures from the compromised keys must no longer be accepted

Attestation ndash Privacy CA Solution (Traditional Credentials)

Issuer

Verifier

Problem Privacy CA does not exist operate 247 security needs to be high ndash a contradiction to 247 no business model (trust relationship w users and verifiers) can link transactions other security requirements would be fulfilled

Privacy CAAIKCertA

EKCertE

AIK CertA SigAIK(m)

Direct Anonymous Attestation (Brickell Camenisch Chen - 2003)

Issuer

VerifierDAA credentials are ldquorandomizablerdquo TPM can transform original credential into new credentials that ldquolooks

likerdquo a fresh credential rarr different randomize credentials cannot be linked (anonymity) rarr still credentials are unforgeable

Direct Anonymous Attestation ndash Rogue TPMs

TPM has been broken and keys have leaked Need to be able to distinguish those keys despite signatures are anonymous

Solution Nym = f(DAA-secret) = ζ DAA-secret mod p where if ζ is random published keys can be detected

protocol is still anonymous if ζ is fixed per verifier eg derived from verifiers name (so-called basename)

verifier can also make frequency analysis rarr signature by the same platform wrt same basename can be linked

protocol is still pseudonymous

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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• Slide 35

Direct Anonymous Attestation ndash Brief History TCPA 044 ndash July 2000 until TCPA 11b ndash February 2002

wout DAA but used Privacy CA Privacy groups criticized Privacy CA solution

TPM 12 ndash July 2003 until Aug 2009 (revision 116) DAA introduced as alternative to Privacy CA goal to make privacy groups happy DAA based on RSA Host part specified in TSS (Trusted Software Stack) Implementation on chips very slow (arithmetic co-processor)

TPM 20 ndash October 2014 Elliptic curve-based DAA ISO standard in 2015 (ISOIEC 11889)

Today Interest in TPM revived Security of mobile devices FIDO authentication

Attestation Scenario

Issuer

(TPM or Platform Manufacturer)

Verifier

(Bank eShop Tax authority hellip)

Problem using traditional certificates all transactions of the same platform become linkable -(

JOIN

SIGN

Privacy barrier

Security Requirements for Attestation

Unforgeability No adversary can create signatures on messages that were never signed by a certified TPMAnonymity signatures by an honest platform are unlinkable (without basename or different basenames)Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this messageRevocation If a TPM is compromised signatures from the compromised keys must no longer be accepted

Attestation ndash Privacy CA Solution (Traditional Credentials)

Issuer

Verifier

Problem Privacy CA does not exist operate 247 security needs to be high ndash a contradiction to 247 no business model (trust relationship w users and verifiers) can link transactions other security requirements would be fulfilled

Privacy CAAIKCertA

EKCertE

AIK CertA SigAIK(m)

Direct Anonymous Attestation (Brickell Camenisch Chen - 2003)

Issuer

VerifierDAA credentials are ldquorandomizablerdquo TPM can transform original credential into new credentials that ldquolooks

likerdquo a fresh credential rarr different randomize credentials cannot be linked (anonymity) rarr still credentials are unforgeable

Direct Anonymous Attestation ndash Rogue TPMs

TPM has been broken and keys have leaked Need to be able to distinguish those keys despite signatures are anonymous

Solution Nym = f(DAA-secret) = ζ DAA-secret mod p where if ζ is random published keys can be detected

protocol is still anonymous if ζ is fixed per verifier eg derived from verifiers name (so-called basename)

verifier can also make frequency analysis rarr signature by the same platform wrt same basename can be linked

protocol is still pseudonymous

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
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• Slide 33
• Slide 34
• Slide 35

Attestation Scenario

Issuer

(TPM or Platform Manufacturer)

Verifier

(Bank eShop Tax authority hellip)

Problem using traditional certificates all transactions of the same platform become linkable -(

JOIN

SIGN

Privacy barrier

Security Requirements for Attestation

Unforgeability No adversary can create signatures on messages that were never signed by a certified TPMAnonymity signatures by an honest platform are unlinkable (without basename or different basenames)Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this messageRevocation If a TPM is compromised signatures from the compromised keys must no longer be accepted

Attestation ndash Privacy CA Solution (Traditional Credentials)

Issuer

Verifier

Problem Privacy CA does not exist operate 247 security needs to be high ndash a contradiction to 247 no business model (trust relationship w users and verifiers) can link transactions other security requirements would be fulfilled

Privacy CAAIKCertA

EKCertE

AIK CertA SigAIK(m)

Direct Anonymous Attestation (Brickell Camenisch Chen - 2003)

Issuer

VerifierDAA credentials are ldquorandomizablerdquo TPM can transform original credential into new credentials that ldquolooks

likerdquo a fresh credential rarr different randomize credentials cannot be linked (anonymity) rarr still credentials are unforgeable

Direct Anonymous Attestation ndash Rogue TPMs

TPM has been broken and keys have leaked Need to be able to distinguish those keys despite signatures are anonymous

Solution Nym = f(DAA-secret) = ζ DAA-secret mod p where if ζ is random published keys can be detected

protocol is still anonymous if ζ is fixed per verifier eg derived from verifiers name (so-called basename)

verifier can also make frequency analysis rarr signature by the same platform wrt same basename can be linked

protocol is still pseudonymous

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
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• Slide 33
• Slide 34
• Slide 35

Security Requirements for Attestation

Unforgeability No adversary can create signatures on messages that were never signed by a certified TPMAnonymity signatures by an honest platform are unlinkable (without basename or different basenames)Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this messageRevocation If a TPM is compromised signatures from the compromised keys must no longer be accepted

Attestation ndash Privacy CA Solution (Traditional Credentials)

Issuer

Verifier

Problem Privacy CA does not exist operate 247 security needs to be high ndash a contradiction to 247 no business model (trust relationship w users and verifiers) can link transactions other security requirements would be fulfilled

Privacy CAAIKCertA

EKCertE

AIK CertA SigAIK(m)

Direct Anonymous Attestation (Brickell Camenisch Chen - 2003)

Issuer

VerifierDAA credentials are ldquorandomizablerdquo TPM can transform original credential into new credentials that ldquolooks

likerdquo a fresh credential rarr different randomize credentials cannot be linked (anonymity) rarr still credentials are unforgeable

Direct Anonymous Attestation ndash Rogue TPMs

TPM has been broken and keys have leaked Need to be able to distinguish those keys despite signatures are anonymous

Solution Nym = f(DAA-secret) = ζ DAA-secret mod p where if ζ is random published keys can be detected

protocol is still anonymous if ζ is fixed per verifier eg derived from verifiers name (so-called basename)

verifier can also make frequency analysis rarr signature by the same platform wrt same basename can be linked

protocol is still pseudonymous

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
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• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Attestation ndash Privacy CA Solution (Traditional Credentials)

Issuer

Verifier

Problem Privacy CA does not exist operate 247 security needs to be high ndash a contradiction to 247 no business model (trust relationship w users and verifiers) can link transactions other security requirements would be fulfilled

Privacy CAAIKCertA

EKCertE

AIK CertA SigAIK(m)

Direct Anonymous Attestation (Brickell Camenisch Chen - 2003)

Issuer

VerifierDAA credentials are ldquorandomizablerdquo TPM can transform original credential into new credentials that ldquolooks

likerdquo a fresh credential rarr different randomize credentials cannot be linked (anonymity) rarr still credentials are unforgeable

Direct Anonymous Attestation ndash Rogue TPMs

TPM has been broken and keys have leaked Need to be able to distinguish those keys despite signatures are anonymous

Solution Nym = f(DAA-secret) = ζ DAA-secret mod p where if ζ is random published keys can be detected

protocol is still anonymous if ζ is fixed per verifier eg derived from verifiers name (so-called basename)

verifier can also make frequency analysis rarr signature by the same platform wrt same basename can be linked

protocol is still pseudonymous

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Direct Anonymous Attestation (Brickell Camenisch Chen - 2003)

Issuer

VerifierDAA credentials are ldquorandomizablerdquo TPM can transform original credential into new credentials that ldquolooks

likerdquo a fresh credential rarr different randomize credentials cannot be linked (anonymity) rarr still credentials are unforgeable

Direct Anonymous Attestation ndash Rogue TPMs

TPM has been broken and keys have leaked Need to be able to distinguish those keys despite signatures are anonymous

Solution Nym = f(DAA-secret) = ζ DAA-secret mod p where if ζ is random published keys can be detected

protocol is still anonymous if ζ is fixed per verifier eg derived from verifiers name (so-called basename)

verifier can also make frequency analysis rarr signature by the same platform wrt same basename can be linked

protocol is still pseudonymous

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
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• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Direct Anonymous Attestation ndash Rogue TPMs

TPM has been broken and keys have leaked Need to be able to distinguish those keys despite signatures are anonymous

Solution Nym = f(DAA-secret) = ζ DAA-secret mod p where if ζ is random published keys can be detected

protocol is still anonymous if ζ is fixed per verifier eg derived from verifiers name (so-called basename)

verifier can also make frequency analysis rarr signature by the same platform wrt same basename can be linked

protocol is still pseudonymous

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

DAA in implementation split operation between host and TPM

proof of secret key ensuring privacy

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
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• Slide 16
• Slide 17
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• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
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• Slide 28
• Slide 29
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• Slide 31
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• Slide 33
• Slide 34
• Slide 35

Direct Anonymous Attestation in TPM V20

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
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• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Overview of Changes from TPM 12 to TPM 20

From RSA groups to elliptic curve groups (faster smaller keys)

TPM V12 DAA protocol spec is split between TPM and TSS (Trusted Software Stack) specs For TPM V20 there is not TSS spec

On the positive side supports many different credential signature schemes (CL q-SDH hellip)

On the negative side

no full specification ndash Chen amp Li 2013 paper hard to match to TPM spec no security proof ndash Chen amp Li 2013 security proof broken current spec not provable secure

PK(x) y = gx

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Difficulty in Security Definitions and Proofs

4 parties amp 4 protocols complex protocol and thus security definition becomes complexrarr

After initial DAA paper (Brickell et al 2004) a number of improved security definitions where published

All of them have issues some of them severe allowing for insecure schemes -(

rarr Need for complete security model amp provably secure schemes

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
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• Slide 28
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• Slide 34
• Slide 35

Simulation-Based Security DefinitionsInteractionwith environment

Interactionwith environment

Functionality (ideal specification)

cryptographic protocolsare run between parties secure if environment

cannot tell apart

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
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• Slide 18
• Slide 19
• Slide 20
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• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Existing Simulation-Based Models for DAA

Brickell Camenisch Chen (2004) Does not output any signature values Prohibits working with signature values in practice

Chen Morrissey Smart (2009) Outputs signatures Signature generation too simplistically modeled to be realizable

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
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• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Property-Based Security DefinitionsInteractionwith environment

cryptographic protocols

Defines security when interacting with cryptographic protocol for each property separately

Eg Non-frameability One cannot create a signature on a message that links to an honest platformrsquos signature when the platform never signed this message

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Existing Property-Based Models for DAA

Brickell Chen Li (2009) Unforgeability not captured trivially forgeable scheme can be proven secure No property for non-frameability

Chen (2010) Extends BCLrsquo09 with non-frameability Same flaws as BCLrsquo09

Bernhard et al (2013) Discusses flaws in all previous models TPM + Host one party Does not cover honest TPM in corrupt Host Security Proof of ldquoPre-DAArdquo does not work for full DAA

Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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Protocols for TPM20

Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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Do we need all these definitions

(1 1 1 1) is a valid credential on any key in Chen Page Smart 2010 ISO 20008 standardized

TPM2 spec contains static DH oracle Larger groups and keys required (Xi et al 2014)

TPM2 should make zero-knowledge proof Problem in hash computation Proof not zero-knowledge

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
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• Slide 3
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• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Comprehensive Model and Secure Protocol

Comprehensive security model in UC framework (ie simulation based) Allows composition by composition theorem Signatures modeled as concrete values that are sent as output TPM and Host separate parties Extensive explanation on why this definition properly captures the security requirements

Provide scheme that realize the functionality Two provably secure instantiation (based on LRSW and q-SDH respectively) As efficient as existing DAA schemes ndash essentially just doing a few details right

Camenisch Drijvers Lehmann 2016 (iacr20151246)

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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• Slide 34
• Slide 35

Realization of Direct Anonymous Attestation in TPM V20

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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• Slide 29
• Slide 30
• Slide 31
• Slide 32
• Slide 33
• Slide 34
• Slide 35

Preliminaries Schnorr Signatures

Given a group ltggt and an element y Є ltggt

Prover wants to convince verifier that she knows x1 x2 st y = gx1 hx2 such that verifier only learns y g and h

t = yc gs1 hs2

Prover

random r1r2

t = gr1 hr2

Verifier

random c

s1 = r1 ndash cx1s2 = r2 - cx2

t

s1 s2

c

PK(αβ) y = gα hβ

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
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• Slide 34
• Slide 35

Prelimiaries ndash Schnorr Signatures

Signing a message m- chose random r1r2 Є Zq and - compute (cs1s2) = (H(gr1 hr2||m) r1 - cx1 r2 - cx2 )

Verifying a signature (cs1s2) on a message m- check c = H(ycgs1hs2||m)

Security- Discrete Logarithm Assumption holds- Hash function H() behaves as a ldquorandom oraclerdquo

From Protocol PK(αβ) y = gα hβ to Signature SPK(α) y = gα (m)

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
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• Slide 35

Bi-Linear Maps

Two groups G Gt of order q (elliptic curve groups) Bi-linear map e GxG Gt rarr with the following properties

Bi-linear e(gahb) = e(gh)ab = e(gbha) Non-degenerate e(gg) ne 1 Efficiently computable (gh) e(gh)rarr

Remarks Given e(gh) and g it is hard to compute h Bi-linear maps makes Decisional Diffie-Hellman in G easy

Recall DDH distinguish between (ggagbgab) and (ggagbgc)

e(gagb) = e(ggab) e(gagb) ne e(ggc)

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

• Slide 1
• Slide 2
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• Slide 35

Public key of signer G Gt of order q generators gh h0 hk and element y

Secret key value x such that y = gx

To sign k messages m1 mk Є Zq

choose random element rs Є Zq

compute A = (gh0sh1

m1 hkmk )1(x+r)

signature is (Ars)

Signature Scheme used to Issue Certificate to TPM

Verification e(Ay)e(Ag)r = e(gh0sh1

m1 hkmk g)

(because e(Agx)e(Ag)r = e(A(x+r)g) we must have A(x+r) = gh0sh1

m1 hkmk )

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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• Slide 35

Signature Scheme used to Issue Certificate to TPM ndash proof of signature

Observed = ce a1

m1 akmk bs mod n

Let A = Aht1 and B = gt1ht2 with randomly chosen t1 t2

To prove ownership of a signature (Ae s) on some on m1 mk execute proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg)

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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• Slide 34
• Slide 35

Using this scheme for TPM 20

TPM secret key m1 Attributes m2 mk

Proof becomes proof protocol

PK(t1t2t3t4rsm1mk) B = gt1ht2 1 =and Brg-t3ht4 and

e(Ay)e(hy)-t1e(Ag)r e(Ag)-t3= e(gh0sh1

m1 hkmkg) and

Nym = H(basename)m1

How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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How the TPM and the Host Sign Jointly (simplyfied)

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t random r2

t = thr2t

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random cc

random r2

t = thr2t

c

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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• Slide 35

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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How the TPM and the Host Sign Jointly (simplyfied)

random r1

t = gr1 t

random c

s1

c

s1= r1 - c x

random r2

t = thr2t

s1 s2

c

s2= r2 - c m

t = ycgs1hs2

PK (x) y = gx

PK (x m) y = gxhm

TPM spec not speced (was TSS spec)

Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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Next Steps

TPM 20 working on fixing security problems trying to unify different schemes spec of full schemes ie also issuer host verifier parts

FIDO anonymous authenticator spec with our without TPM 20 reference implementation underway (aim at open sourcing it)

Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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Conclusions

Device authentication more relevant than ever

Provable security matters ndash a number of standards have issues It often takes far longer than one would expect amp still not done

Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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Thanks Questions

iacr20151246jcazurichibmcomJanCamenisch

ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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ReferencesBernhard D Fuchsbauer G Ghadafi E Smart N Warinschi B Anonymous attestation with user-controlled linkability International Journal of Information Security 12(3) (2013)Brickell E Camenisch J Chen L Direct anonymous attestation ACM CCS 2004Brickell E Chen L Li J Simplified security notions of direct anonymous attestation and a concrete scheme from pairings International Journal of Information Security 8(5) (2009) Camenisch J Lysyanskaya A Signature schemes and anonymous credentials from bilinear maps CRYPTO 2004Camenisch J Drijvers M Lehmann A Anonymous Attestation Using the Strong Diffie-Hellman Assumption Revisited TRUST 2016 1-20Camenisch J Drijvers M Lehmann A Universally Composable Direct Anonymous Attestation Public Key Cryptography (2) 2016 234-264Chen L Morrissey P Smart N DAA Fixing the pairing based protocols ePrint Archive Report 2009198Chen L A DAA scheme requiring less tpm resources Information Security and Cryptology 2010Chen L Morrissey P Smart N On proofs of security for DAA schemes Provable Security 2008Chen L Page D Smart N On the design and implementation of an efficient DAA scheme Smart Card Research and Advanced Application 2010 Chen L Li J Flexible and scalable digital signatures in TPM 20 ACM CCS 2013Lysyanskaya A Rivest RL Sahai A Wolf S Pseudonym systems SAC 1999Xi L Yang K Zhang Z Feng D DAA-related APIs in TPM 20 revisited Trust and Trustworthy Computing 2014

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