Skip to main content

Computer-Aided Cryptographic Proofs

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7406))

Abstract

EasyCrypt is an automated tool that supports the machine-checked construction and verification of security proofs of cryptographic systems, and that has been used to verify emblematic examples of public-key encryption schemes, digital signature schemes, hash function designs, and block cipher modes of operation. The purpose of this paper is to motivate the role of computer-aided proofs in the broader context of provable security and to illustrate the workings of EasyCrypt through simple introductory examples.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Audebaud, P., Paulin-Mohring, C.: Proofs of randomized algorithms in COQ. Sci. Comput. Program. 74(8), 568–589 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Backes, M., Barthe, G., Berg, M., Grégoire, B., Kunz, C., Skoruppa, M., Zanella Béguelin, S.: Verified security of Merkle-Damgård. In: 25rd IEEE Computer Security Foundations Symposium, CSF 2012. IEEE Computer Society (2012)

    Google Scholar 

  3. Barthe, G., Grégoire, B., Heraud, S., Olmedo, F., Zanella Béguelin, S.: Verified Indifferentiable Hashing into Elliptic Curves. In: Degano, P., Guttman, J.D. (eds.) POST 2012. LNCS, vol. 7215, pp. 209–228. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Barthe, G., Grégoire, B., Heraud, S., Zanella Béguelin, S.: Computer-Aided Security Proofs for the Working Cryptographer. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 71–90. Springer, Heidelberg (2011)

    Google Scholar 

  5. 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 

  6. Bellare, M.: Practice-Oriented Provable-Security. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 221–231. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  7. Bellare, M., Canetti, R., Krawczyk, H.: Keying Hash Functions for Message Authentication. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 1–15. Springer, Heidelberg (1996)

    Google Scholar 

  8. Bellare, M., Kilian, J., Rogaway, P.: The Security of Cipher Block Chaining. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 341–358. Springer, Heidelberg (1994)

    Google Scholar 

  9. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: 1st ACM Conference on Computer and Communications Security, CCS 1993, pp. 62–73. ACM, New York (1993)

    Chapter  Google Scholar 

  10. Bellare, M., Rogaway, P.: Entity Authentication and Key Distribution. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 232–249. Springer, Heidelberg (1994)

    Google Scholar 

  11. 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 

  12. Bleichenbacher, D.: Chosen Ciphertext Attacks against Protocols Based on the RSA Encryption Standard PKCS #1. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 1–12. Springer, Heidelberg (1998)

    Google Scholar 

  13. Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. 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)

    Article  MathSciNet  Google Scholar 

  16. Damgård, I.: A “proof-reading” of Some Issues in Cryptography. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 2–11. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Deng, Y., Du, W.: Logical, metric, and algorithmic characterisations of probabilistic bisimulation. Technical Report CMU-CS-11-110, Carnegie Mellon University (March 2011)

    Google Scholar 

  18. Dent, A.W.: Fundamental problems in provable security and cryptography. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364(1849), 3215–3230 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, pp. 293–302. IEEE Computer Society, Washington (2008)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  22. Harrison, J.: Formal proof – theory and practice. Notices of the American Mathematical Society 55(11), 1395–1406 (2008)

    MathSciNet  MATH  Google Scholar 

  23. Jonsson, B., Yi, W., Larsen, K.G.: Probabilistic extensions of process algebras. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, pp. 685–710. Elsevier, Amsterdam (2001)

    Google Scholar 

  24. Kocher, P.C.: Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)

    Google Scholar 

  25. Kocher, P.C., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)

    Google Scholar 

  26. Manger, J.: A Chosen Ciphertext Attack on RSA Optimal Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1 v2.0. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 230–238. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  27. Maurer, U., Renner, R., Holenstein, C.: Indifferentiability, Impossibility Results on Reductions, and Applications to the Random Oracle Methodology. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  28. Pollack, R.: How to believe a machine-checked proof. In: Twenty-Five Years of Constructive Type Theory: Proceedings of a Congress Held in Venice, October 1995. Oxford Logic Guides, vol. 36. Oxford University Press (1998)

    Google Scholar 

  29. Ristenpart, T., Shacham, H., Shrimpton, T.: Careful with Composition: Limitations of the Indifferentiability Framework. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 487–506. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  30. Rogaway, P.: Practice-oriented provable security and the social construction of cryptography (2009) (unpublished essay)

    Google Scholar 

  31. Shannon, C.: Communication theory of secrecy systems. Bell System Technical Journal 28, 656–715 (1949)

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  33. 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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barthe, G., Crespo, J.M., Grégoire, B., Kunz, C., Zanella Béguelin, S. (2012). Computer-Aided Cryptographic Proofs. In: Beringer, L., Felty, A. (eds) Interactive Theorem Proving. ITP 2012. Lecture Notes in Computer Science, vol 7406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32347-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32347-8_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32346-1

  • Online ISBN: 978-3-642-32347-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics