Formal security proofs with minimal fuss: Implicit computational complexity at work

David Nowak (1, 2) , Yu Zhang (3)

1 2XS - Extra Small Extra Safe
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 LCS - State Key Laboratory of Computer Science [Beijing]

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.

Mots clés: lambda-calculus; safe recursion; probabilistic computation; cryptography

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]; Cryptographie et sécurité [cs.CR]; Langage de programmation [cs.PL]

David Nowak, Yu Zhang. Formal security proofs with minimal fuss: Implicit computational complexity at work. Information and Computation, 2015, 241, pp.96-113. ⟨10.1016/j.ic.2014.10.008⟩. ⟨hal-01144726⟩