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Another Look at “Provable Security”. II

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Progress in Cryptology - INDOCRYPT 2006 (INDOCRYPT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4329))

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Abstract

We discuss the question of how to interpret reduction arguments in cryptography. We give some examples to show the subtlety and difficulty of this question.

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References

  1. Abdalla, M., Pointcheval, D.: Simple password-based encrypted key exchange protocols. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 191–208. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Ajtai, M., Dwork, C.: A public-key cryptosystem with worst-case/average-case equivalence. In: Proc. 29th Symp. Theory of Computing, pp. 284–293. ACM, New York (1997)

    Google Scholar 

  3. Alexi, W., Chor, B., Goldreich, O., Schnorr, C.P.: RSA and Rabin functions: Certain parts are as hard as the whole. SIAM J. Computing 17, 194–209 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  4. Barreto, P., Libert, B., McCullagh, N., Quisquater, J.-J.: Efficient and provably-secure identity-based signatures and signcryption from bilinear maps. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 515–532. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Bellare, M.: Practice-oriented provable-security. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 221–231. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  6. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: Proc. First Annual Conf. Computer and Communications Security, pp. 62–73. ACM, New York (1993)

    Chapter  Google Scholar 

  7. Bellare, M., Rogaway, P.: Optimal asymmetric encryption — how to encrypt with RSA. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  8. Blackburn, S., Paterson, K.: Cryptanalysis of a message authentication code due to Cary and Venkatesan. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 446–453. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudo-random number generator. SIAM J. Computing 15, 364–383 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  10. Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Computing 13, 850–864 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  11. Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Boneh, D., Venkatesan, R.: Breaking RSA may not be equivalent to factoring. In: Advances in Cryptology – Eurocrypt 1998. LNCS, vol. 1233, pp. 59–71. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  14. Brown, D.: Generic groups, collision resistance, and ECDSA. Designs, Codes and Cryptography 35, 119–152 (2005)

    Article  MATH  Google Scholar 

  15. Brown, D.: On the provable security of ECDSA. In: Blake, I., Seroussi, G., Smart, N. (eds.) Advances in Elliptic Curve Cryptography, pp. 21–40. Cambridge University Press, Cambridge (2005)

    Chapter  Google Scholar 

  16. Brown, D.: Breaking RSA may be as difficult as factoring, http://eprint.iacr.org/2005/380

  17. Brown, D.: Unpublished communication (February 2006)

    Google Scholar 

  18. Cary, M., Venkatesan, R.: A message authentication code based on unimodular matrix groups. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 500–512. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. Coron, J.-S.: On the exact security of full domain hash. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 229–235. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  20. Coron, J.-S.: Optimal security proofs for PSS and other signature schemes. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 272–287. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. Eastlake, D., Crocker, S., Schiller, J.: RFC 1750 – Randomness Recommendations for Security, Available from: http://www.ietf.org/rfc/rfc1750.txt

  22. Fischlin, R., Schnorr, C.P.: Stronger security proofs for RSA and Rabin bits. J. Cryptology 13, 221–244 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Gennaro, R.: An improved pseudo-random generator based on the discrete log problem. J. Cryptology 18, 91–110 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  24. Howgrave-Graham, N., Dyer, J., Gennaro, R.: Pseudo-random number generation on the IBM 4758 Secure Crypto Coprocessor. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 93–102. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  25. Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: 10th ACM Conf. Computer and Communications Security, pp. 155–164 (2003)

    Google Scholar 

  26. Knuth, D.: Seminumerical Algorithms. In: Art of Computer Programming, 3rd edn., vol. 2, Addison-Wesley, Reading (1997)

    Google Scholar 

  27. Koblitz, N., Menezes, A.: Another look at provable security. J. Cryptology (to appear), Available from: http://eprint.iacr.org/2004/152

  28. Mackenzie, P., Patel, S.: Hard bits of the discrete log with applications to password authentication. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 209–226. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  29. 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 

  30. Nguyen, P.Q., Stern, J.: Cryptanalysis of the Ajtai–Dwork cryptosystem. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 223–242. Springer, Heidelberg (1998)

    Google Scholar 

  31. Nguyen, P.Q., Stern, J.: The two faces of lattices in cryptology. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 146–180. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  32. Paillier, P., Vergnaud, D.: Discrete-log-based signatures not be equivalent to discrete log. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 1–20. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  33. Pointcheval, D., Stern, J.: Security proofs for signature schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 387–398. Springer, Heidelberg (1996)

    Google Scholar 

  34. Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptology 13, 361–396 (2000)

    Article  MATH  Google Scholar 

  35. Schnorr, C.P.: Efficient signature generation for smart cards. J. Cryptology 4, 161–174 (1991)

    MATH  MathSciNet  Google Scholar 

  36. Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)

    Google Scholar 

  37. Shoup, V.: Why chosen ciphertext security matters, IBM Research Report RZ 3076 (#93122) (23/11/1998)

    Google Scholar 

  38. Shoup, V.: OAEP reconsidered. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 239–259. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  39. Sidorenko, A.: Unpublished communication (March 2006)

    Google Scholar 

  40. Sidorenko, A., Schoenmakers, B.: Concrete security of the Blum–Blum–Shub pseudorandom generator. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol. 3796, pp. 355–375. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  41. Vazirani, U.V., Vazirani, V.V.: Efficient and secure pseudo-random number generation. In: Proc. IEEE 25th Annual Symp. Foundations of Computer Science, pp. 458–463 (1984)

    Google Scholar 

  42. Yao, A.: Theory and applications of trapdoor functions. In: Proc. IEEE 23rd Annual Symp. Foundations of Computer Science, pp. 80–91 (1982)

    Google Scholar 

  43. Young, A., Yung, M.: Malicious Cryptography: Exposing Cryptovirology. Wiley, Chichester (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Washington,  

    Neal Koblitz

  2. Department of Combinatorics & Optimization, University of Waterloo,  

    Alfred Menezes

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  1. Neal Koblitz
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  2. Alfred Menezes
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Editors and Affiliations

  1. Indian Statistical Institute, 205, B.T. Road, Kolkata, India

    Rana Barua

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600, Eindhoven, MB, Netherlands

    Tanja Lange

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Koblitz, N., Menezes, A. (2006). Another Look at “Provable Security”. II. In: Barua, R., Lange, T. (eds) Progress in Cryptology - INDOCRYPT 2006. INDOCRYPT 2006. Lecture Notes in Computer Science, vol 4329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11941378_12

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  • DOI: https://doi.org/10.1007/11941378_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49767-7

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