On formal verification of arithmetic-based cryptographic primitives

Details On formal verification of arithmetic-based cryptographic primitives On formal verification of arithmetic-based cryptographic primitives

2009-04-07

arxiv.org/abs/0904.1110v1

In Information Security and Cryptology - ICISC 2008, 11th International Conference, Seoul, Korea, December 3-5, 2008, Proceedi

Computer Science

Cryptography and Security

13 pages

Scientific paper

10.1007/978-3-642-00730-9_23

Cryptographic primitives are fundamental for information security: they are used as basic components for cryptographic protocols or public-key cryptosystems. In many cases, their security proofs consist in showing that they are reducible to computationally hard problems. Those reductions can be subtle and tedious, and thus not easily checkable. On top of the proof assistant Coq, we had implemented in previous work a toolbox for writing and checking game-based security proofs of cryptographic primitives. In this paper we describe its extension with number-theoretic capabilities so that it is now possible to write and check arithmetic-based cryptographic primitives in our toolbox. We illustrate our work by machine checking the game-based proofs of unpredictability of the pseudo-random bit generator of Blum, Blum and Shub, and semantic security of the public-key cryptographic scheme of Goldwasser and Micali.

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