Cryptology ePrint Archive: Report 2010/230

A calculus for game-based security proofs

David Nowak and Yu Zhang

Abstract: The game-based approach to security proofs in cryptography is a widely-used methodology for writing proofs rigorously. However a unifying language for writing games is still missing. In this paper we show how CSLR, a probabilistic lambda-calculus with a type system that guarantees that computations are probabilistic polynomial time, can be equipped with a notion of game indistinguishability. This allows us to de ne cryptographic constructions, e ective adversaries, security notions, computational assumptions, game transformations, and game-based security proofs in the uni ed framework provided by CSLR. Our code for cryptographic constructions is close to implementation in the sense that we do not assume primitive uniform distributions but use a realistic algorithm to approximate them. We illustrate our calculus on cryptographic constructions for public-key encryption and pseudorandom bit generation.

Category / Keywords: foundations / game-based proofs, implicit complexity, computational indistinguishability

Date: received 23 Apr 2010, last revised 25 Apr 2010

Contact author: yu zhang at gmail com

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Version: 20100428:135303 (All versions of this report)

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