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

ISBN-10: 3540435530

ISBN-13: 9783540435532

ISBN-10: 3540460357

ISBN-13: 9783540460350

This e-book constitutes the refereed court cases of the overseas convention at the idea and alertness of Cryptographic thoughts, EUROCRYPT 2002, held in Amsterdam, The Netherlands, in April/May 2002.

The 33 revised complete papers provided have been rigorously reviewed and chosen from a complete of 122 submissions. The papers are prepared in topical sections on cryptanalysis, public-key encryption, info concept and new types, implementational research, flow ciphers, electronic signatures, key trade, modes of operation, traitor tracing and id-based encryption, multiparty and multicast, and symmetric cryptology.

**Read Online or Download Advances in Cryptology — EUROCRYPT 2002: International Conference on the Theory and Applications of Cryptographic Techniques Amsterdam, The Netherlands, April 28 – May 2, 2002 Proceedings PDF**

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**Additional info for Advances in Cryptology — EUROCRYPT 2002: International Conference on the Theory and Applications of Cryptographic Techniques Amsterdam, The Netherlands, April 28 – May 2, 2002 Proceedings**

**Example text**

Lett. 6(1999), no. 3-4, 287–291. 3. S. Birman, Braids, links and the mapping class group, Ann. Math. Studies 82, Princeton Univ. Press, 1974. 4. S. H. J. Lee, A new approaches to the world and conjugacy problem in the braid groups, Adv. Math. 139(1998), no. 2, 322–353. 5. S. H. J. Lee, The inﬁmum, supremum and geodesic length of a braid conjugacy class, Adv. Math. 164(2001), no. 1, 41–56. 6. C. H. J. W. H. Cheon, An Eﬃcient Implementation of Braid Groups, Advances in Cryptology—ASIACRYPT 2001, (Gold Coast, Queensland, Australia), 144–156, Lecture Notes in Comput.

One also ensures that l does not divide q ni − 1, for all “small” values of i. The GHS attack is as follows. One takes an elliptic curve deﬁned, as above, over Fqn , with a large subgroup of prime order l. We assume the curve is given by an equation of the form E : Y 2 + XY = X 3 + aX 2 + b where a ∈ {0, 1}, b ∈ K. We may assume that a ∈ {0, 1} since r and n are odd. Then one constructs the Weil restriction of scalars WE/k of E over k, this is an n-dimensional abelian variety over k. The variety WE/k is then intersected with n − 1 carefully chosen hyperplanes so as to obtain a hyperelliptic curve C over the ﬁeld k.

This is a restatement of the Convexity Theorem in Appendix C. By Theorem 2 and Theorem 3, we can solve any MSCP in ﬁnite time. But the computational complexity of a naive implementation is exponential with respect to the braid index n and involves the cardinality of the set C inf (a1 , . . , ar ). There seems to be no previous result concerning the cardinality of C inf (a1 , . . , ar ). If the instances are extremely simple, for example when all ai ’s are positive braids, then the set C inf (a1 , .

### Advances in Cryptology — EUROCRYPT 2002: International Conference on the Theory and Applications of Cryptographic Techniques Amsterdam, The Netherlands, April 28 – May 2, 2002 Proceedings by Rosario Gennaro, Daniele Micciancio (auth.), Lars R. Knudsen (eds.)

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