signcryption parshuram budhathoki department of mathematical sciences florida atlantic university...
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Signcryption
Parshuram BudhathokiDepartment of Mathematical Sciences
Florida Atlantic University
April 18, 2013
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Motivation:
Confidentiality :
Integrity :
Authentication :
Nonrepudiation :
Keeping information secret from all other than those who are authorized to see it.
Ensuring that the information has not been altered by unauthorized entities.
The assurance that the communicating party is the one that it claims to be.
Preventing the denial of previous commitments or actions.
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Motivation:
Confidential and Authenticate
Traditional Method “Signature- Then- Seal”
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Motivation:
Confidentiality :
How do we get these things in modern cryptography ?
Signature Scheme
Encryption Scheme
Nonrepudiation :
Integrity :
Authentication :
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Signature Scheme
RSA
Schnorr
DSS
Others …
Motivation:How do we get these things in modern cryptography ?
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Encryption Scheme
RSA
ElGamal
Others …
Motivation:How do we get these things in modern cryptography ?
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In 1997 Yulian Zheng proposed a separate primitive called Signcryption.
Is it possible to deliver messages of varying length in a secure and authenticated way with an expense less than that required by “Signature-Then-Encryption ” ?
Motivation:
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Outline :
• Why Signcryption ?
• Signcryption
• Shortening ElGamal-Based Signatures.
• Secure Signcryption Scheme.
• Signcryption Scheme by Y. Zheng.
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Why Signcryption ?
Cost of Signcryption < Cost of Signature + Cost of Encryption
1. Computational cost2. Communication overhead
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1. Computational cost
We estimate computational cost by counting the number of operations involved :• Private key encryption and decryption • Hashing• addition• Multiplication• Division• Exponentiation
Why Signcryption ?
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2. Communication overhead
In addition to computational cost, digital signature and encryption based on public key cryptography also require extra bits to be appended to a message. We call these extra redundant bits the communication overhead involved.
Why Signcryption ?
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Signcryption
Gen Security Parameter
key-pair Public
Private
SC Private keysender , Message, RID
C= SCPrivate Key ( Message, RID )
DSC DSCPrivate Key ( C, SID )Private keyreceiver , C , SID
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Shortening ElGamal-Based Signatures:
• Key Generation: Choose x randomly from {1, …, p-1} Public key = gx Private key = x
Let p is a large prime, q is a large prime factor of p-1 and g is an integer from {1, …, p-1}.
Let h: {1,..., p-1} x {0,1}* {1, ..., p-1} be a hash function.
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• Sign : Choose y randomly from {1, …, p-1} r = h( gy mod p, M) s = y / ( r + x ) mod p , where M = message
Signature = < r, s >
Let p is a large prime, q is a large prime factor of p-1 and g is an integer from {1, …, p-1}.
Let h: {1,..., p-1} x {0,1}* {1, ..., p-1} be a hash function.
Shortening ElGamal-Based Signatures:
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Let p is a large prime, q is a large prime factor of p-1 and g is an integer from {1, …, p-1}.
Let h: {1,..., p-1} x {0,1}* {1, ..., p-1} be a hash function.
• Verify : Compute k = ( gx ∙ gr )s mod p Accept if r = h( k, m)
Shortening ElGamal-Based Signatures:
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Secure Scheme:
Secure Signature Scheme :
Unforgeable under adaptively chosen message attack.
Secure Encryption Scheme :
Indistinguishable against adaptively chosen cipher attack.
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Unforgeable : It is computationally infeasible for an adaptive attacker to create a signcrypted text.
Non-repudiation : It is computationally feasible for a third party to settle a dispute between signer and receiver where signer denies the fact that he/she is the originator of a signcrypted text.
Confidential: It is computationally infeasible for an adaptive attacker to gain any partial information on the contents of a signcrypted text.
Secure Signcryption Scheme:
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YZ- Signcryption Scheme:
Gen : Using this algorithm sender and receiver choose their key-pair. Let x, y from [1, ..., q-1] are sender’s and receiver’s private keys and S= gx and R= gy are their respective public keys.
p : a large prime ( public )q : a large prime factor of p-1 ( public )g : a ( random ) integer in [1, ..., p-1] with order q mod p ( public )h : a one-way hash function ( public )
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YZ- Signcryption Scheme: p : a large prime ( public )q : a large prime factor of p-1 ( public )g : a ( random ) integer in [1, ..., p-1] with order q mod p ( public )h : a one-way hash function ( public )S : Sender’s public keyR : Receiver’s public key
SC : Pick r randomly from [1, ..., q-1] 1. compute k = Rr mod p. Split k into k1 and k2 of appropriate length. 2. n= h(M, k2 ), where M=message 3. s= r/( n + x ) mod q 4. c = E_k1 ( M ) , where E := Encryption in AES Signcrypted text = < c, n, s>
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YZ- Signcryption Scheme:
DSC : Recover k from n, s, g, p, S and R: 1. k = ( S ∙ gh )s ・ y mod p 2. Split k into k1 and k2 3. M = D_k1 ( c ) , Where D := Decryption in AES 4. Accept M as a valid message if h(M, k2) = n
p : a large prime ( public )q : a large prime factor of p-1 ( public )g : a ( random ) integer in [1, ..., p-1] with order q mod p ( public )h : a one-way hash function ( public )S : Sender’s public keyR : Receiver’s public key
NOTE : D_k1 ( E_k1 (M)) = M4/18/13
Security parameters|p|, |q|, |h( . )|
Saving in comp. cost
Saving in comm. overhead
768, 152, 80 50% 76.8%
1024, 160, 80 50% 81.01%
2048, 192, 96 50% 87.7%
4096, 256, 128 50% 91.0%
8192, 320, 160 50% 94.0%
10240, 320, 160 50% 96.0%
Cost of Signcryption vs. Cost of Sign-Then-Encryption
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