Advances in Cryptology — EUROCRYPT 2002: International by Rosario Gennaro, Daniele Micciancio (auth.), Lars R. Knudsen

By Rosario Gennaro, Daniele Micciancio (auth.), Lars R. Knudsen (eds.)

This booklet constitutes the refereed court cases of the foreign convention at the concept and alertness of Cryptographic thoughts, EUROCRYPT 2002, held in Amsterdam, The Netherlands, in April/May 2002.
The 33 revised complete papers awarded have been rigorously reviewed and chosen from a complete of 122 submissions. The papers are equipped in topical sections on cryptanalysis, public-key encryption, info idea and new versions, implementational research, circulate ciphers, electronic signatures, key alternate, modes of operation, traitor tracing and id-based encryption, multiparty and multicast, and symmetric cryptology.

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Ar ∈ Bn , define C inf (a1 , . . , ar ) as the set of all (u1 , . . , ur ) such that inf(ui ) ≥ inf(ai ) for all i and there exists some w ∈ Bn satisfying ui = w−1 ai w for all i simultaneously. Theorem 2. Let (a1 , . . , ar ) and (c1 , . . , cr ) be an instance of an MSCP in Bn and x a positive braid such that x−1 ai x = ci for all i. Assume that ai ’s and ci ’s are already in the left canonical form. Then we can compute positive braid x0 24 Sang Jin Lee and Eonkyung Lee and (c1 , . .

On Infor. , 39, 1639–1646, 1993. 15. A. Menezes and M. Qu. Analysis of the Weil descent attack of Gaudry, Hess and Smart. Topics in Cryptology - CT-RSA 2001, Springer-Verlag LNCS 2020, 308–318, 2001. 16. S. Pohlig and M. Hellman. An improved algorithm for computing logarithms over GF (p) and its cryptographic significance. IEEE Trans. on Infor. , 24, 106–110, 1978. 17. J. Pollard. Monte Carlo methods for index computations mod p. Math. , 32, 918–924, 1978. 18. P. Smart. How secure are elliptic curves over composite extension fields?

The ideal b in Stage 2 will have norm at most O( ∆). The smooth representation of the ideal equivalent to a will have at most O(log ∆) not necessarily distinct factors in it, each factor corresponding to an isogeny of degree at most L. Hence, the mapping of points from E1 to E2 , given the smooth representation of the ideal equivalent to a, can be performed in time polynomial in log q n . 4 Finding Vulnerable Curves Theorem 2 shows that there is a set of possible values for b such that the elliptic curves Y 2 + XY = X 3 + b and Y 2 + XY = X 3 + X 2 + b have a specific small value for m.

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