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 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 conception and new versions, implementational research, movement ciphers, electronic signatures, key alternate, modes of operation, traitor tracing and id-based encryption, multiparty and multicast, and symmetric cryptology.

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Additional resources 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

Whenever Proposition 1 is applied in the loop, the word-length of x0 strictly increases and its final length is bounded above by |x|. So the algorithm stops in at most |x| repetitions of the loop. All the computations involved is to compute simple conjugations such as HaH −1 , a ∈ Bn and H a permutation braid, which can be done in time O(n(log n)|a|) and simple multiplications of the form Hx0 , which can be done in time O(n(log n)|x0 |). 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’.

Cr ) such that (c1 , . . , cr ) ∈ C inf (a1 , . . , ar ) and ci = x0 ci x−1 0 for all i, in time proportional to r (|ai | + |ci |) , n(log n)|x| |x| + (1) i=1 where | · | denotes the word-length in generators. Moreover x = x1 x0 for some positive braid x1 , in particular the word-length of x1 is less than that of x. Proof. We exhibit an algorithm that computes x0 and hence (c1 , . . , cr ). Input: (a1 , . . , ar ), (c1 , . . , cr ) ∈ (Bn )r . Initialization: x0 = e(identity braid), ci = ci for all i.

The isogeny) would enable one to solve the discrete logarithm. This approach might have both malicious and beneficial applications. We achieve the first point as follows. Given an elliptic curve E1 over Fqn with N = #E1 (Fqn ) the strategy is to search over all elliptic curves which are vulnerable to the GHS attack (using the method of Section 4) until one is found which has N points (this is checked by ‘exponentiating’ a random point). Once such an ‘easy’ curve is found one can construct an isogeny explicitly using the method of Section 3, which is an improved version of the algorithm of Galbraith [8].

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