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Merkle Puzzles Are Optimal — An O(n2)-Query Attack on Any Key Exchange from a Random Oracle

  • Boaz Barak
  • Mohammad Mahmoody-Ghidary
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5677)

Abstract

We prove that every key exchange protocol in the random oracle model in which the honest users make at most n queries to the oracle can be broken by an adversary making O(n2) queries to the oracle. This improves on the previous \(\Tilde{\Omega}(n^6)\) query attack given by Impagliazzo and Rudich (STOC ’89), and answers an open question posed by them. Our bound is optimal up to a constant factor since Merkle (CACM ’78) gave a key exchange protocol that can easily be implemented in this model with n queries and cannot be broken by an adversary making o(n2) queries.

Keywords

Bipartite Graph Random Oracle Random Oracle Model Oracle Query Random Edge 
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.

References

  1. 1.
    Merkle, R.: Secure communications over insecure channels. Communications of the ACM 21(4), 294–299 (1978)CrossRefGoogle Scholar
  2. 2.
    Cachin, M.: Unconditional security against memory-bounded adversaries. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 292–306. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Biham, E., Goren, Y.J., Ishai, Y.: Basing weak public-key cryptography on strong one-way functions. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 55–72. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  4. 4.
    Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. In: Proc. 30th STOC, pp. 209–218. ACM, New York (1998)Google Scholar
  5. 5.
    Diffie, W., Hellman, M.: New directions in cryptography. IEEE Transactions on Information Theory IT-22(6), 644–654 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Proceedings of the First Annual Conference on Computer and Communications Security, November 1993, pp. 62–73. ACM, New York (1993)Google Scholar
  8. 8.
    Impagliazzo, R., Rudich, S.: Limits on the provable consequences of one-way permutations. In: Proc. 21st STOC, pp. 44–61. ACM, New York (1989); Full version available from Russell Impagliazzo’s home pageGoogle Scholar
  9. 9.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Annual Symposium on Theory of Computing, May 22–24, pp. 212–219 (1996)Google Scholar
  10. 10.
    Bennett, C.H., Brassard, G., Ekert, A.: Quantum cryptography. SCIAM: Scientific American 267 (1992)Google Scholar
  11. 11.
    Brassard, G., Salvail, L.: Quantum merkle puzzles. In: International Conference on Quantum, Nano and Micro Technologies (ICQNM), pp. 76–79. IEEE Computer Society, Los Alamitos (2008)CrossRefGoogle Scholar
  12. 12.
    Barak, B., Mahmoody-Ghidary, M.: Merkle Puzzles are Optimal. Arxiv preprint arXiv:0801.3669v1 (2008); Preliminary version of this paper. Version 1 contained a bug that is fixed in this versionGoogle Scholar
  13. 13.
    Sotakova, M.: Breaking one-round key-agreement protocols in the random oracle model. Cryptology ePrint Archive, Report 2008/053 (2008), http://eprint.iacr.org/

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Boaz Barak
    • 1
  • Mohammad Mahmoody-Ghidary
    • 1
  1. 1.Department of Computer SciencePrinceton UniversityUSA

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