Formal security proofs with minimal fuss: Implicit computational complexity at work
We show how implicit computational complexity can be used in order to increase confidence in game-based security proofs in cryptography. For this purpose we extend CSLR, a probabilistic lambda-calculus with a type system that guarantees the existence of a probabilistic polynomial-time bound on compu...
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| Published in: | Information and computation Vol. 241; pp. 96 - 113 |
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| Language: | English |
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01.04.2015
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| Abstract | We show how implicit computational complexity can be used in order to increase confidence in game-based security proofs in cryptography. For this purpose we extend CSLR, a probabilistic lambda-calculus with a type system that guarantees the existence of a probabilistic polynomial-time bound on computations. This allows us to define cryptographic constructions, feasible adversaries, security notions, computational assumptions, game transformations, and game-based security proofs in a unified framework. We also show that the standard practice of cryptographers, ignoring that polynomial-time Turing machines cannot generate all uniform distributions, is actually sound. We illustrate our calculus on cryptographic constructions for public-key encryption and pseudorandom bit generation. |
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| AbstractList | We show how implicit computational complexity can be used in order to increase confidence in game-based security proofs in cryptography. For this purpose we extend CSLR, a probabilistic lambda-calculus with a type system that guarantees the existence of a probabilistic polynomial-time bound on computations. This allows us to define cryptographic constructions, feasible adversaries, security notions, computational assumptions, game transformations, and game-based security proofs in a unified framework. We also show that the standard practice of cryptographers, ignoring that polynomial-time Turing machines cannot generate all uniform distributions, is actually sound. We illustrate our calculus on cryptographic constructions for public-key encryption and pseudorandom bit generation. |
| Author | Nowak, David Zhang, Yu |
| Author_xml | – sequence: 1 givenname: David surname: Nowak fullname: Nowak, David organization: JFLI, CNRS & The University of Tokyo, Japan – sequence: 2 givenname: Yu surname: Zhang fullname: Zhang, Yu organization: State Key Laboratory for Computer Science, ISCAS, China |
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| Keywords | Probabilistic computation Cryptography Safe recursion Lambda-calculus cryptography safe recursion lambda-calculus probabilistic computation |
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| Title | Formal security proofs with minimal fuss: Implicit computational complexity at work |
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