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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Bibliographic Details
Published in:Information and computation Vol. 241; pp. 96 - 113
Main Authors: Nowak, David, Zhang, Yu
Format: Journal Article
Language:English
Published: Elsevier Inc 01.04.2015
Elsevier
Subjects:
Computational Complexity
Computer Science
Cryptography
Cryptography and Security
Lambda-calculus
Logic in Computer Science
Probabilistic computation
Programming Languages
Safe recursion
Probabilistic computation
Cryptography
Safe recursion
Lambda-calculus
cryptography
safe recursion
lambda-calculus
probabilistic computation
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary: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.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2014.10.008