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Formal Certification of ElGamal Encryption

A Gentle Introduction to CertiCrypt

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Formal Aspects in Security and Trust (FAST 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5491))

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Abstract

CertiCrypt [1] is a framework that assists the construction of machine-checked cryptographic proofs that can be automatically verified by third parties. To date, CertiCrypt has been used to prove formally the exact security of widely studied cryptographic systems, such as the OAEP padding scheme and the Full Domain Hash digital signature scheme. The purpose of this article is to provide a gentle introduction to CertiCrypt. For concreteness, we focus on a simple but illustrative example, namely the semantic security of the Hashed ElGamal encryption scheme in both, the standard and the random oracle model.

This work has been partially supported by the ANR project SCALP.

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References

  1. 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. ACM Press, New York (2009)

    Google Scholar 

  2. Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  3. Stern, J.: Why provable security matters? In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656. Springer, Heidelberg (2003)

    Google Scholar 

  4. 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)

    Chapter  Google Scholar 

  5. Halevi, S.: A plausible approach to computer-aided cryptographic proofs. Cryptology ePrint Archive, Report 2005/181 (2005)

    Google Scholar 

  6. Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. Cryptology ePrint Archive, Report 2004/332 (2004)

    Google Scholar 

  7. The Coq development team: The Coq Proof Assistant Reference Manual v8.2 (2008), http://coq.inria.fr

  8. Sabelfeld, A., Sands, D.: A per model of secure information flow in sequential programs. Higher-Order and Symbolic Computation 14(1), 59–91 (2001)

    Article  MATH  Google Scholar 

  9. Audebaud, P., Paulin-Mohring, C.: Proofs of randomized algorithms in Coq. Science of Computer Programming (2008)

    Google Scholar 

  10. Benton, N.: Simple relational correctness proofs for static analyses and program transformations. In: Proceedings of the 31th ACM Symposium on Principles of Programming Languages, pp. 14–25. ACM Press, New York (2004)

    Google Scholar 

  11. Jonsson, B., Larsen, K.G., Yi, W.: Probabilistic extensions of process algebras. In: Handbook of Process Algebra, pp. 685–711. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  12. Nowak, D.: A framework for game-based security proofs. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, pp. 319–333. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Barthe, G., Cederquist, J., Tarento, S.: A machine-checked formalization of the generic model and the random oracle model. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS, vol. 3097, pp. 385–399. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. 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)

    Chapter  Google Scholar 

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Barthe, G., Grégoire, B., Heraud, S., Zanella Béguelin, S. (2009). Formal Certification of ElGamal Encryption. In: Degano, P., Guttman, J., Martinelli, F. (eds) Formal Aspects in Security and Trust. FAST 2008. Lecture Notes in Computer Science, vol 5491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01465-9_1

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  • DOI: https://doi.org/10.1007/978-3-642-01465-9_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01464-2

  • Online ISBN: 978-3-642-01465-9

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