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 e-book constitutes the refereed complaints of the foreign convention at the concept and alertness of Cryptographic options, EUROCRYPT 2002, held in Amsterdam, The Netherlands, in April/May 2002.
The 33 revised complete papers provided have been conscientiously reviewed and chosen from a complete of 122 submissions. The papers are equipped in topical sections on cryptanalysis, public-key encryption, details conception and new versions, implementational research, movement ciphers, electronic signatures, key trade, modes of operation, traitor tracing and id-based encryption, multiparty and multicast, and symmetric cryptology.

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Example text

Bs ) are pure, then the induced permutation is nothing more than the identity. Hence, we can consider the following simple cases. 1. Choose (a1 , . . , ar ) in Bn and (b1 , . . , bs ) in the pure braid group. Then the induced permutation of x = W (b1 , . . , bs ) is the identity but it is impossible 22 Sang Jin Lee and Eonkyung Lee to list all y = V (a1 , . . , ar ) because the equation y −1 bi y = di gives no information about πy . 2. Choose (a1 , . . , ar ) and (b1 , . . , bs ) so that the induced permutations of ai ’s fix {1, .

So the whole complexity is (1). Note that the ai ’s are much simpler than ci ’s [1] and that the newly obtained braids ci ’s are at least as simple as ai ’s in terms of ‘inf’. Now we have simple instance (a1 , . . , ar ) and (c1 , . . , cr ). The natural question is how to solve the MSCP for this new instance. It uses a variant of the Convexity Theorem [4,9]. See Appendix C. Theorem 3. Given (c1 , . . , cr ) ∈ C inf (a1 , . . , ar ), there exists a chain of elements in C inf (a1 , . . , ar ) from (a1 , .

J. edu/˜mccarthy/research/. 19. W. Miller, The maximum order of an element of a finite symmetric group, Amer. Math. Monthly 94(1987), no. 6, 497–506. 20. R. Morton, The multivariable Alexander polynomial for a closed braid, Lowdimensional topology (Funchal, 1998), 167–172, Contemp. , 233, Amer. Math. , Providence, RI, 1999. The Commutator Key Agreement Protocol Based on Braid Groups A 27 Left-Weighted For a positive braid P , the starting set S(P ) and the finishing set F (P ) is defined as follows.

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