Advances in Cryptology — ASIACRYPT 2002: 8th International by Arjen K. Lenstra, Adi Shamir, Jim Tomlinson (auth.), Yuliang

By Arjen K. Lenstra, Adi Shamir, Jim Tomlinson (auth.), Yuliang Zheng (eds.)

This e-book constitutes the refereed lawsuits of the eighth overseas convention at the concept and alertness of Cryptology and data protection, ASIACRYPT 2002, held in Singapore, in December 2002.
The 34 revised complete papers awarded including invited contributions have been conscientiously reviewed and chosen from 173 submissions at the foundation of 875 overview stories. The papers are equipped in topical sections on public key cryptography, authentication, conception, block ciphers, dispensed cryptography, cryptanalysis, public key cryptanalysis, mystery sharing, electronic signatures, functions, Boolean features, key administration, and ID-based cryptography.

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Remark 3 describes how to enforce U1 , U2 ∈ QRN . A Variant of the Cramer-Shoup Cryptosystem for Groups of Unknown Order 31 Assumption: (Target collision resistance of H) Let FH be a family of hash functions {0, 1}∗ → ZZm , for m ≤ pq. Consider the following experiment: 1. Fix an input T for H (the “target”). 2. Randomly choose H from the family FH . , an input T = T such that H(T ) = H(T ). As a minor abuse of notation, we write “H is target collision resistant” (“TCresistant”) to indicate that H has been chosen from such a family FH .

Com 13. L. Montgomery, A block Lanczos algorithm for finding dependencies over GF(2), Proceedings Eurocrypt’95, LNCS 925, Springer-Verlag 1995, 106–120 14. gov/encryption/kms 15. D. html 16. P. Schnorr, A. Shamir, An Optimal Sorting Algorithm for Mesh Connected Computers, Proceedings 16th ACM Symposium on Theory of Computing, 255–263, 1986 17. G. Villard, Further analysis of Coppersmith’s block Wiedemann algorithm for the solution of sparse linear systems (extended abstract), Proceedings 1997 International Symposium on Symbolic and Algebraic Computation, ACM Press, 32–39, 1997 Analysis of Bernstein’s Factorization Circuit 25 18.

Thus, an efficient generic ACC attack against the scheme does not necessarily reduce to a practical solution for the CDH problem for G. As explained above, the reduction in the current paper is quite efficient, using linearly many moderately simple operations (such as exponentiations mod N ), but no potentially complex operation (such as the DDH oracle in [13]). Also note that we do not assume the hash function H to be TC-resistant, for Theorem 4, in contrast to [13, Theorem 3]. On the other hand, the random oracle security in the current paper is based on the factoring assumption, not on the CDH assumption.

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