Abstract
CertiCrypt is a general framework to certify the security of cryptographic primitives in the Coq proof assistant. CertiCrypt adopts the code-based paradigm, in which the statement of security, and the hypotheses under which it is proved, are expressed using probabilistic programs. It provides a set of programming language tools (observational equivalence, relational Hoare logic, semantics-preserving program transformations) to assist in constructing proofs. Earlier publications of CertiCrypt provide an overview of its architecture and main components, and describe its application to signature and encryption schemes. This paper describes programming language techniques that arise specifically in cryptographic proofs. The techniques have been developed to complete a formal proof of IND-CCA security of the OAEP padding scheme. In this paper, we illustrate their usefulness for showing the PRP/PRF Switching Lemma, a fundamental cryptographic result that bounds the probability of an adversary to distinguish a family of pseudorandom functions from a family of pseudorandom permutations.
This work was partially supported by French ANR SESUR-012, SCALP, Spanish project TIN2009-14599 DESAFIOS 10, Madrid Regional project S2009TIC-1465 PROMETIDOS, and Microsoft Research-INRIA Joint Centre.
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References
Affeldt, R., Tanaka, M., Marti, N.: Formal proof of provable security by game-playing in a proof assistant. In: Susilo, W., Liu, J.K., Mu, Y. (eds.) ProvSec 2007. LNCS, vol. 4784, pp. 151–168. Springer, Heidelberg (2007)
Audebaud, P., Paulin-Mohring, C.: Proofs of randomized algorithms in Coq. Science of Computer Programming 74(8), 568–589 (2009)
Barthe, G., Grégoire, B., Zanella Béguelin, S.: Formal certification of code-based cryptographic proofs. In: Proceedings of the 36th ACM Symposium on Principles of Programming Languages, pp. 90–101. ACM Press, New York (2009)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Proceedings of the 1st ACM Conference on Computer and Communications Security, pp. 62–73. ACM Press, New York (1993)
Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006)
Briggs, P., Cooper, K.D., Torczon, L.: Rematerialization. In: Proceedings of the ACM SIGPLAN’92 Conference on Programming Language Design and Implementation, pp. 311–321. ACM Press, New York (1992)
Corin, R., den Hartog, J.: A probabilistic Hoare-style logic for game-based cryptographic proofs. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 252–263. Springer, Heidelberg (2006)
Fujisaki, E., Okamoto, T., Pointcheval, D., Stern, J.: RSA-OAEP is secure under the RSA assumption. Journal of Cryptology 17(2), 81–104 (2004)
Hurd, J., McIver, A., Morgan, C.: Probabilistic guarded commands mechanized in HOL. Theor. Comput. Sci. 346(1), 96–112 (2005)
Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pp. 44–61. ACM Press, New York (1989)
Leroy, X.: Formal certification of a compiler back-end, or: programming a compiler with a proof assistant. In: Proceedings of the 33rd ACM Symposium Principles of Programming Languages, pp. 42–54. ACM Press, New York (2006)
McIver, A., Morgan, C.: Abstraction, Refinement, and Proof for Probabilistic Systems. Springer, Heidelberg (2005)
Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. Cryptology ePrint Archive, Report 2004/332 (2004), http://eprint.iacr.org/2004/332
Stern, J.: Why provable security matters? In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 449–461. Springer, Heidelberg (2003)
The Coq development team: The Coq Proof Assistant Reference Manual Version 8.2 (2009), http://coq.inria.fr
Tristan, J.B., Leroy, X.: Verified validation of lazy code motion. In: Proceedings of the 2009 ACM SIGPLAN Conference on Programming Language Design and Implementation, pp. 316–326. ACM Press, New York (2009)
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Barthe, G., Grégoire, B., Zanella Béguelin, S. (2010). Programming Language Techniques for Cryptographic Proofs. In: Kaufmann, M., Paulson, L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14052-5_10
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