Advertisement

Computational Soundness of Equational Theories (Tutorial)

  • Steve Kremer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4912)

Abstract

We study the link between formal and cryptographic models for security protocols in the presence of passive and adaptive adversaries. We first describe the seminal result by Abadi and Rogaway and shortly discuss some of its extensions. Then we describe a general model for reasoning about the soundness of implementations of equational theories. We illustrate this model on several examples of computationally sound implementations of equational theories.

Keywords

Equational Theory Symbolic Model Symmetric Encryption Modular Exponentiation Sort Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abadi, M., Baudet, M., Warinschi, B.: Guessing attacks and the computational soundness of static equivalence. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Abadi, M., Cortier, V.: Deciding knowledge in security protocols under equational theories. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 46–58. Springer, Heidelberg (2004)Google Scholar
  3. 3.
    Abadi, M., Fournet, C.: Mobile values, new names, and secure communications. In: Proc. 28th Annual ACM Symposium on Principles of Programming Languages (POPL 2001), pp. 104–115. ACM Press, New York (2001)CrossRefGoogle Scholar
  4. 4.
    Abadi, M., Rogaway, P.: Reconciling two views of cryptography (the computational soundness of formal encryption). In: Watanabe, O., Hagiya, M., Ito, T., van Leeuwen, J., Mosses, P.D. (eds.) TCS 2000. LNCS, vol. 1872, pp. 3–22. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Abadi, M., Rogaway, P.: Reconciling two views of cryptography (the computational soundness of formal encryption). Journal of Cryptology 15(2), 103–127 (2002)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Adão, P., Bana, G., Herzog, J., Scedrov, A.: Soundness of formal encryption in the presence of key-cycles. In: di Vimercati, S.d.C., Syverson, P.F., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 374–396. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Adão, P., Bana, G., Herzog, J., Scedrov, A.: Soundness of formal encryption in the presence of key-cycles. In: di Vimercati, S.d.C., Syverson, P.F., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 374–396. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Adão, P., Bana, G., Scedrov, A.: Computational and information-theoretic soundness and completeness of formal encryption. In: Proc. 18th IEEE Computer Security Foundations Workshop (CSFW 2005), pp. 170–184 (2005)Google Scholar
  9. 9.
    Backes, M., Pfitzmann, B., Waidner, M.: A composable cryptographic library with nested operations. In: Proc. 10th ACM Conference on Computer and Communications Security (CCS 2003) (2003)Google Scholar
  10. 10.
    Baudet, M., Cortier, V., Kremer, S.: Computationally sound implementations of equational theories against passive adversaries. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 652–663. Springer, Heidelberg (2005)Google Scholar
  11. 11.
    Blanchet, B.: Automatic proof of strong secrecy for security protocols. In: Proc. 25th IEEE Symposium on Security and Privacy (SSP 2004), pp. 86–100 (2004)Google Scholar
  12. 12.
    Bresson, E., Lakhnech, Y., Mazaré, L., Warinschi, B.: A generalization of ddh with applications to protocol analysis and computational soundness. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 482–499. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Chevassut, O., Fouque, P.-A., Gaudry, P., Pointcheval, D.: Key derivation and randomness extraction. Technical Report 2005/061, Cryptology ePrint Archive (2005), http://eprint.iacr.org/
  14. 14.
    Corin, R., Doumen, J., Etalle, S.: Analysing password protocol security against off-line dictionary attacks. ENTCS 121, 47–63 (2005)Google Scholar
  15. 15.
    Cortier, V., Delaune, S., Lafourcade, P.: A survey of algebraic properties used in cryptographic protocols. Journal of Computer Security 14(1), 1–43 (2006)Google Scholar
  16. 16.
    Dwork, C., Naor, M., Reingold, O., Stockmeyer, L.J.: Magic functions. J. ACM 50(6), 852–921 (2003)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Garcia, F.D., van Rossum, P.: Sound computational interpretation of symbolic hashes in the standard model. In: Yoshiura, H., Sakurai, K., Rannenberg, K., Murayama, Y., Kawamura, S.-i. (eds.) IWSEC 2006. LNCS, vol. 4266, pp. 33–47. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Kremer, S., Mazaré, L.: Adaptive soundness of static equivalence. In: Biskup, J., López, J. (eds.) ESORICS 2007. LNCS, vol. 4734, pp. 610–625. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    Laud, P., Corin, R.: Sound computational interpretation of formal encryption with composed keys. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. LNCS, vol. 2971, pp. 55–66. Springer, Heidelberg (2004)Google Scholar
  21. 21.
    Micciancio, D., Panjwani, S.: Adaptive security of symbolic encryption. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 169–187. Springer, Heidelberg (2005)Google Scholar
  22. 22.
    Micciancio, D., Warinschi, B.: Completeness theorems for the Abadi-Rogaway logic of encrypted expressions. Journal of Computer Security 12(1), 99–129 (2004)Google Scholar
  23. 23.
    Micciancio, D., Warinschi, B.: Soundness of formal encryption in the presence of active adversaries. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 133–151. Springer, Heidelberg (2004)Google Scholar
  24. 24.
    Phan, D.H., Pointcheval, D.: About the security of ciphers (semantic security and pseudo-random permutations). In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 185–200. Springer, Heidelberg (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Steve Kremer
    • 1
  1. 1.LSV, ENS Cachan & CNRS & INRIA Futurs 

Personalised recommendations