Advertisement

The Computational SLR: A Logic for Reasoning about Computational Indistinguishability

  • Yu Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5608)

Abstract

Computational indistinguishability is a notion in complexity-theoretic cryptography and is used to define many security criteria. However, in traditional cryptography, proving computational indistinguishability is usually informal and becomes error-prone when cryptographic constructions are complex. This paper presents a formal proof system based on an extension of Hofmann’s SLR language, which can capture probabilistic polynomial-time computations through typing and is sufficient for expressing cryptographic constructions. We in particular define rules that justify directly the computational indistinguishability between programs and prove that these rules are sound with respect to the set-theoretic semantics, hence the standard definition of security. We also show that it is applicable in cryptography by verifying, in our proof system, Goldreich and Micali’s construction of pseudorandom generator.

Keywords

Proof System Cryptographic Protocol Typing Rule Pseudorandom Generator Security Criterion 
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.
    Backes, M., Berg, M., Unruh, D.: A formal language for cryptographic pseudocode. In: 4th Workshop on Formal and Computational Cryptography, FCC 2008 (2008)Google Scholar
  2. 2.
    Barthe, G., Grégoire, B., Janvier, R., 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 (2009)Google Scholar
  3. 3.
    Bellantoni, S., Cook, S.A.: A new recursion-theoretic characterization of the polytime functions. Computational Complexity 2, 97–110 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bellare, M., Rogaway, P.: Code-based game-playing proofs and the security of triple encryption. Cryptology ePrint Archive, Report 2004/331 (2004)Google Scholar
  5. 5.
    Blanchet, B.: A computationally sound mechanized prover for security protocols. In: IEEE Symposium on Security and Privacy (S&P 2006), pp. 140–154 (2006)Google Scholar
  6. 6.
    Goldreich, O.: The Foundations of Cryptography: Basic Tools. Cambridge University Press, Cambridge (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Hofmann, M.: A mixed modal/linear lambda calculus with applications to bellantoni-cook safe recursion. In: Nielsen, M. (ed.) CSL 1997. LNCS, vol. 1414, pp. 275–294. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    Hofmann, M.: Safe recursion with higher types and BCK-algebra. Annals of Pure and Applied Logic 104(1-3), 113–166 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Impagliazzo, R., Kapron, B.M.: Logics for reasoning about cryptographic constructions. Journal of Computer and System Sciences 72(2), 286–320 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Mitchell, J.C., Mitchell, M., Scedrov, A.: A linguistic characterization of bounded oracle computation and probabilistic polynomial time. In: 39th Annual Symposium on Foundations of Computer Science (FOCS 1998), pp. 725–733 (1998)Google Scholar
  11. 11.
    Mitchell, J.C., Ramanathan, A., Scedrov, A., Teague, V.: A probabilistic polynomial-time process calculus for the analysis of cryptographic protocols. Theoretical Computer Science 353(1-3), 118–164 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Moggi, E.: Notions of computation and monads. Information and Computation 93(1), 55–92 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Ramsey, N., Pfeffer, A.: Stochastic lambda calculus and monads of probability distributions. In: 29th SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL 2002), pp. 154–165 (2002)Google Scholar
  15. 15.
    Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. Cryptology ePrint Archive, Report 2004/332 (2004)Google Scholar
  16. 16.
    Zhang, Y.: The computational SLR: a logic for reasoning about computational indistinguishability. Cryptology ePrint Archive, Report 2008/434 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yu Zhang
    • 1
    • 2
  1. 1.Laboratory of Computer ScienceInstitute of Software, CASBeijingChina
  2. 2.FITMacau University of Science and Technology, Macau SARChina

Personalised recommendations