Computer-Aided Security Proofs for the Working Cryptographer

  • Gilles Barthe
  • Benjamin Grégoire
  • Sylvain Heraud
  • Santiago Zanella Béguelin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6841)

Abstract

We present EasyCrypt, an automated tool for elaborating security proofs of cryptographic systems from proof sketches–compact, formal representations of the essence of a proof as a sequence of games and hints. Proof sketches are checked automatically using off-the-shelf SMT solvers and automated theorem provers, and then compiled into verifiable proofs in the CertiCrypt framework. The tool supports most common reasoning patterns and is significantly easier to use than its predecessors. We argue that EasyCrypt is a plausible candidate for adoption by working cryptographers and illustrate its application to security proofs of the Cramer-Shoup and Hashed ElGamal cryptosystems.

Keywords

Provable security verifiable security game-based proofs Cramer-Shoup cryptosystem ElGamal encryption 

References

  1. 1.
    Backes, M., Maffei, M., Unruh, D.: Computationally sound verification of source code. In: 17th ACM Conference on Computer and Communications Security, CCS 2010, pp. 387–398. ACM, New York (2010)Google Scholar
  2. 2.
    Barthe, G., D’Argenio, P., Rezk, T.: Secure information flow by self-composition. In: 17th IEEE Workshop on Computer Security Foundations, CSFW 2004, pp. 100–114. IEEE Computer Society, Washington (2004)CrossRefGoogle Scholar
  3. 3.
    Barthe, G., Daubignard, M., Kapron, B., Lakhnech, Y.: Computational indistinguishability logic. In: 17th ACM Conference on Computer and Communications Security, CCS 2010, pp. 375–386. ACM, New York (2010)Google Scholar
  4. 4.
    Barthe, G., Grégoire, B., Heraud, S., Zanella Béguelin, S.: Formal certification of ElGamal encryption. A gentle introduction to CertiCrypt. In: Degano, P., Guttman, J., Martinelli, F. (eds.) FAST 2008. LNCS, vol. 5491, pp. 1–19. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Barthe, G., Grégoire, B., Lakhnech, Y., Zanella Béguelin, S.: Beyond provable security verifiable IND-CCA security of OAEP. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 180–196. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Barthe, G., Grégoire, B., Zanella Béguelin, S.: Formal certification of code-based cryptographic proofs. In: 36th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2009, pp. 90–101. ACM, New York (2009)Google Scholar
  7. 7.
    Barthe, G., Hedin, D., Zanella Béguelin, S., Grégoire, B., Heraud, S.: A machine-checked formalization of Sigma-protocols. In: 23rd IEEE Computer Security Foundations Symposium, CSF 2010, pp. 246–260. IEEE Computer Society, Los Alamitos (2010)CrossRefGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Bhargavan, K., Fournet, C., Gordon, A.D.: Modular verification of security protocol code by typing. In: 37th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2010, pp. 445–456. ACM, New York (2010)Google Scholar
  10. 10.
    Blanchet, B., Jaggard, A.D., Scedrov, A., Tsay, J.K.: Computationally sound mechanized proofs for basic and public-key Kerberos. In: 15th ACM Conference on Computer and Communications Security, CCS 2008, pp. 87–99. ACM, New York (2008)Google Scholar
  11. 11.
    Blanchet, B.: A computationally sound mechanized prover for security protocols. In: 27th IEEE Symposium on Security and Privacy, S&P 2006, pp. 140–154. IEEE Computer Society, Los Alamitos (2006)Google Scholar
  12. 12.
    Blanchet, B., Pointcheval, D.: Automated security proofs with sequences of games. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 537–554. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Conchon, S., Contejean, E., Kanig, J., Lescuyer, S.: CC(X): Semantic combination of congruence closure with solvable theories. Electronic Notes in Theoretical Computer Science 198(2), 51–69 (2008)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Cremers, C.: The scyther tool: Verification, falsification, and analysis of security protocols. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 414–418. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
    Detlefs, D., Nelson, G., Saxe, J.B.: Simplify: A theorem prover for program checking. Tech. Rep. HPL-2003-148, HP Laboratories Palo Alto (2003)Google Scholar
  16. 16.
    Filliâtre, J.C.: The WHY verification tool: Tutorial and Reference Manual Version 2.28 (2010), http://why.lri.fr
  17. 17.
    Halevi, S.: A plausible approach to computer-aided cryptographic proofs. Cryptology ePrint Archive, Report 2005/181 (2005)Google Scholar
  18. 18.
    Jonsson, B., Yi, W., Larsen, K.G.: Probabilistic extensions of process algebras. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 685–710. Elsevier, Amsterdam (2001)Google Scholar
  19. 19.
    Paulson, L.C.: The inductive approach to verifying cryptographic protocols. J. of Comput. Secur. 6(1-2), 85–128 (1998)Google Scholar
  20. 20.
    Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. Cryptology ePrint Archive, Report 2004/332 (2004)Google Scholar
  21. 21.
    Stump, A.: Proof checking technology for satisfiability modulo theories. Electr. Notes Theor. Comput. Sci. 228, 121–133 (2009)CrossRefGoogle Scholar
  22. 22.
    The Coq development team: The Coq Proof Assistant Reference Manual Version 8.3 (2010), http://coq.inria.fr
  23. 23.
    Zanella Béguelin, S.: Formal Certification of Game-Based Cryptographic Proofs. Ph.D. thesis, Ecole Nationale Supérieure des Mines de Paris – Mines ParisTech (2010)Google Scholar
  24. 24.
    Zanella Béguelin, S., Grégoire, B., Barthe, G., Olmedo, F.: Formally certifying the security of digital signature schemes. In: 30th IEEE Symposium on Security and Privacy, S&P 2009, pp. 237–250. IEEE Computer Society, Los Alamitos (2009)CrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Gilles Barthe
    • 1
  • Benjamin Grégoire
    • 2
  • Sylvain Heraud
    • 2
  • Santiago Zanella Béguelin
    • 1
  1. 1.IMDEA Software InstituteMadridSpain
  2. 2.INRIA Sophia Antipolis-MéditerranéeFrance

Personalised recommendations