resources in cryptography
TRANSCRIPT
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Resources in Cryptography
Ed Blakey
http://users.ox.ac.uk/~quee1871/
Information Security as a Resource
13.x.2011
Oxford University Computer Science Department
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Disclaimer!
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Computational complexity.
Complexity: how resources scale with respect to |x|. Says something: (directly) about efficiency of M, and
(indirectly) about difficulty of computing f.
output input
M
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Computational complexity.
Complexity: how resources scale with respect to |x|. Says something: (directly) about efficiency of M, and
(indirectly) about difficulty of computing f.
output input
x f(x)
f
M
![Page 5: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/5.jpg)
Computational complexity.
Complexity: how resources scale with respect to |x|. Says something: (directly) about efficiency of M, and
(indirectly) about difficulty of computing f.
output input
x f(x)
f
M
![Page 6: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/6.jpg)
Computational complexity.
Complexity: how resources scale with respect to |x|. Says something: (directly) about efficiency of M, and
(indirectly) about difficulty of computing f.
output input
x f(x)
f
M
![Page 7: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/7.jpg)
Computational complexity.
Complexity: how resources scale with respect to |x|. Says something: (directly) about efficiency of M, and
(indirectly) about difficulty of computing f.
Resources
output input
x f(x)
f
M
![Page 8: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/8.jpg)
Computational complexity.
Complexity: how resources scale with respect to |x|. Says something: (directly) about efficiency of M, and
(indirectly) about difficulty of computing f.
Resources
output input
x f(x)
f
M
![Page 9: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/9.jpg)
Computational complexity.
Complexity: how resources scale with respect to |x|. Says something: (directly) about efficiency of M, and
(indirectly) about difficulty of computing f.
Resources
output input
x f(x)
f
M
![Page 10: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/10.jpg)
Standard resources.
Bounds in terms of time and space.
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Standard resources.
Bounds in terms of time and space.
NP P
EXP AC0
PH
coNP
BPP
PSPACE
NC
P/poly
L
PP
BQP
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Standard resources.
Bounds in terms of time and space.
NP P
EXP AC0
PH
coNP
BPP
PSPACE
NC
P/poly
L
PP
BQP
non-determinism
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Standard resources.
Bounds in terms of time and space.
NP P
EXP AC0
PH
coNP
BPP
PSPACE
NC
P/poly
L
PP
BQP
non-determinism
parallelism
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Standard resources.
Bounds in terms of time and space.
NP P
EXP AC0
PH
coNP
BPP
PSPACE
NC
P/poly
L
PP
BQP
non-determinism
parallelism
![Page 15: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/15.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
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Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 17: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/17.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 18: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/18.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 19: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/19.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 20: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/20.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 21: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/21.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 22: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/22.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
Photo credit: Department of Energy/Coherent Inc Laser Group
![Page 23: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/23.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 24: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/24.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 25: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/25.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 26: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/26.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 27: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/27.jpg)
Non-standard resources
e.g., precision.
Precision complexity.
Detail deferred: A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
![Page 28: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/28.jpg)
Resources…
…for computation.
…for cryptographic protocols.
time space
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Resources…
…for computation.
…for cryptographic protocols.
time space
precision
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Resources…
…for computation.
…for cryptographic protocols.
time space
precision material cost
thermodynamic cost
energy
mass
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Resources…
…for computation.
…for cryptographic protocols.
time space
precision material cost
thermodynamic cost
energy
mass etc.
![Page 32: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/32.jpg)
Resources…
…for computation.
…for cryptographic protocols.
time space
precision material cost
thermodynamic cost
energy
mass etc.
![Page 33: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/33.jpg)
Resources…
…for computation.
…for cryptographic protocols.
time space
precision material cost
thermodynamic cost
energy
mass etc.
![Page 34: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/34.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
![Page 35: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/35.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
![Page 36: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/36.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
![Page 37: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/37.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob…
![Page 38: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/38.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob…
![Page 39: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/39.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob…
![Page 40: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/40.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
![Page 41: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/41.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob…
![Page 42: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/42.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob…
![Page 43: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/43.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob…
Earday Obbay…
![Page 44: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/44.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob…
Earday Obbay…
![Page 45: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/45.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob… Dear Bob…
Earday Obbay…
![Page 46: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/46.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob… Dear Bob…
Earday Obbay…
Key
![Page 47: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/47.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Dear Bob… Dear Bob…
Earday Obbay…
Key
![Page 48: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/48.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Decrypt
Dear Bob… Dear Bob…
Earday Obbay…
Key
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Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Decrypt
Dear Bob… Dear Bob…
Earday Obbay…
Key
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Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
![Page 51: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/51.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Key gen
![Page 52: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/52.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Key gen
Public Private
![Page 53: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/53.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Key gen
Public Private
![Page 54: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/54.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Key gen
Dear Bob…
Public Private
![Page 55: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/55.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 56: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/56.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 57: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/57.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 58: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/58.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 59: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/59.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 60: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/60.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 61: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/61.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 62: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/62.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 63: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/63.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 64: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/64.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 65: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/65.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 66: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/66.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 67: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/67.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
![Page 68: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/68.jpg)
Communication.
Symmetric-key cryptography.
Public-key cryptography.
Computation. Communication. Information — inc. side-channel info.
?
Key gen
Earday Obbay…
Dear Bob…
Public Private
What we want to capture
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Resource of ‘security’.
Temptation: to produce some (1-D) quantity (that depends on |key|, say) that’s
� large when things are difficult for Eve but easy for Alice and Bob, and
� small otherwise. However, boils down to standard comp. complexity of Eve’s decryption computation. Instead, maybe want a (multi-D) quantity that reflects
� computational difficulty for Eve,
� computational ease for Alice and Bob,
� information aspects of protocol,
� etc.
![Page 70: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/70.jpg)
Resource of ‘security’.
Temptation: to produce some (1-D) quantity (that depends on |key|, say) that’s
� large when things are difficult for Eve but easy for Alice and Bob, and
� small otherwise. However, boils down to standard comp. complexity of Eve’s decryption computation. Instead, maybe want a (multi-D) quantity that reflects
� computational difficulty for Eve,
� computational ease for Alice and Bob,
� information aspects of protocol,
� etc.
![Page 71: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/71.jpg)
Resource of ‘security’.
Temptation: to produce some (1-D) quantity (that depends on |key|, say) that’s
� large when things are difficult for Eve but easy for Alice and Bob, and
� small otherwise. However, boils down to standard comp. complexity of Eve’s decryption computation. Instead, maybe want a (multi-D) quantity that reflects
� computational difficulty for Eve,
� computational ease for Alice and Bob,
� information aspects of protocol,
� etc.
e.g. factorization
![Page 72: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/72.jpg)
Resource of ‘security’.
Temptation: to produce some (1-D) quantity (that depends on |key|, say) that’s
� large when things are difficult for Eve but easy for Alice and Bob, and
� small otherwise. However, boils down to standard comp. complexity of Eve’s decryption computation. Instead, maybe want a (multi-D) quantity that reflects
� computational difficulty for Eve,
� computational ease for Alice and Bob,
� information aspects of protocol,
� etc.
e.g. factorization
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Resource of ‘security’.
Temptation: to produce some (1-D) quantity (that depends on |key|, say) that’s
� large when things are difficult for Eve but easy for Alice and Bob, and
� small otherwise. However, boils down to standard comp. complexity of Eve’s decryption computation. Instead, maybe want a (multi-D) quantity that reflects
� computational difficulty for Eve,
� computational ease for Alice and Bob,
� information aspects of protocol,
� etc.
e.g. factorization
i.e. ‘what we want to capture’ (prev. slide)
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Maintaining generality.
Problem with using concepts like ‘difficulty for Eve’:
— assumes rigid goody/baddy roles seen in cryptographic protocols,
but not necessarily seen in wider information-theory setting. Instead, consider how hard agents must compute, what they know, etc. without using a priori goody/baddy labels. Then work out which agent is Alice, which is Bob, which is Eve based on difficulty, etc.
![Page 75: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/75.jpg)
Maintaining generality.
Problem with using concepts like ‘difficulty for Eve’:
— assumes rigid goody/baddy roles seen in cryptographic protocols,
but not necessarily seen in wider information-theory setting. Instead, consider how hard agents must compute, what they know, etc. without using a priori goody/baddy labels. Then work out which agent is Alice, which is Bob, which is Eve based on difficulty, etc.
(complexity) (information)
![Page 76: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/76.jpg)
Maintaining generality.
Problem with using concepts like ‘difficulty for Eve’:
— assumes rigid goody/baddy roles seen in cryptographic protocols,
but not necessarily seen in wider information-theory setting. Instead, consider how hard agents must compute, what they know, etc. without using a priori goody/baddy labels. Then work out which agent is Alice, which is Bob, which is Eve based on difficulty, etc.
(complexity) (information)
![Page 77: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/77.jpg)
Primitives.
One-way fn. Trapdoor fn. Pseudorandom no. gen. etc.
Goody/baddy-free approach ⇒ dealing at level of primitives rather than
dealing with full-blown protocols with predefined roles. So, want to consider trade-offs between security and not only resources, but also primitives.
![Page 78: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/78.jpg)
Primitives.
One-way fn. Trapdoor fn. Pseudorandom no. gen. etc.
Goody/baddy-free approach ⇒ dealing at level of primitives rather than
dealing with full-blown protocols with predefined roles. So, want to consider trade-offs between security and not only resources, but also primitives.
![Page 79: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/79.jpg)
Primitives.
One-way fn. Trapdoor fn. Pseudorandom no. gen. etc.
Goody/baddy-free approach ⇒ dealing at level of primitives rather than
dealing with full-blown protocols with predefined roles. So, want to consider trade-offs between security and not only resources, but also primitives.
![Page 80: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/80.jpg)
Primitives.
One-way fn. Trapdoor fn. Pseudorandom no. gen. etc.
Goody/baddy-free approach ⇒ dealing at level of primitives rather than
dealing with full-blown protocols with predefined roles. So, want to consider trade-offs between security and not only resources, but also primitives.
![Page 81: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/81.jpg)
Idea.
Want a framework that accommodates such things as
� computational resources (⇒ complexity),
� communication resources,
� primitives and
� availability of information.
Gives us a better chance of spotting (e.g.) side-channel attacks than (say) a complexity-only view.
Can view a process (computation, comm., etc.) as having costs in these ‘dimensions’. Many such processes/entities have ‘thickness’ in only one dimension;
if this were true of all entities, then framework would decompose and give nothing new. But some special entities—like security—straddle more than one dimension,
and make the structure non-trivial and useful.
![Page 82: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/82.jpg)
Idea.
Want a framework that accommodates such things as
� computational resources (⇒ complexity),
� communication resources,
� primitives and
� availability of information.
Gives us a better chance of spotting (e.g.) side-channel attacks than (say) a complexity-only view.
Can view a process (computation, comm., etc.) as having costs in these ‘dimensions’. Many such processes/entities have ‘thickness’ in only one dimension;
if this were true of all entities, then framework would decompose and give nothing new. But some special entities—like security—straddle more than one dimension,
and make the structure non-trivial and useful.
![Page 83: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/83.jpg)
Idea.
Want a framework that accommodates such things as
� computational resources (⇒ complexity),
� communication resources,
� primitives and
� availability of information.
Gives us a better chance of spotting (e.g.) side-channel attacks than (say) a complexity-only view.
Can view a process (computation, comm., etc.) as having costs in these ‘dimensions’. Many such processes/entities have ‘thickness’ in only one dimension;
if this were true of all entities, then framework would decompose and give nothing new. But some special entities—like security—straddle more than one dimension,
and make the structure non-trivial and useful.
![Page 84: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/84.jpg)
Idea.
Want a framework that accommodates such things as
� computational resources (⇒ complexity),
� communication resources,
� primitives and
� availability of information.
Gives us a better chance of spotting (e.g.) side-channel attacks than (say) a complexity-only view.
Can view a process (computation, comm., etc.) as having costs in these ‘dimensions’. Many such processes/entities have ‘thickness’ in only one dimension;
if this were true of all entities, then framework would decompose and give nothing new. But some special entities—like security—straddle more than one dimension,
and make the structure non-trivial and useful.
![Page 85: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/85.jpg)
Idea.
Want a framework that accommodates such things as
� computational resources (⇒ complexity),
� communication resources,
� primitives and
� availability of information.
Gives us a better chance of spotting (e.g.) side-channel attacks than (say) a complexity-only view.
Can view a process (computation, comm., etc.) as having costs in these ‘dimensions’. Many such processes/entities have ‘thickness’ in only one dimension;
if this were true of all entities, then framework would decompose and give nothing new. But some special entities—like security—straddle more than one dimension,
and make the structure non-trivial and useful.
![Page 86: Resources in Cryptography](https://reader030.vdocuments.mx/reader030/viewer/2022012716/61af02ab4da6b30a8773fac9/html5/thumbnails/86.jpg)
Questions?
Discussion.
Precision complexity reference:
A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
This research was funded by the EPSRC grant:
Complexity and Decidability in Unconventional Computational Models (EP/G003017/1) Ed Blakey http://users.ox.ac.uk/~quee1871/
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Questions?
Discussion.
Precision complexity reference:
A Model-Independent Theory of Computational Complexity http://users.ox.ac.uk/~quee1871/thesis.pdf
This research was funded by the EPSRC grant:
Complexity and Decidability in Unconventional Computational Models (EP/G003017/1) Ed Blakey http://users.ox.ac.uk/~quee1871/