By Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery (auth.), Bart Preneel (eds.)

ISBN-10: 3540455396

ISBN-13: 9783540455394

ISBN-10: 3540675175

ISBN-13: 9783540675174

This e-book constitutes the refereed court cases of the foreign convention at the idea and alertness of Cryptographic suggestions, EUROCRYPT 2000, held in Bruges, Belgium, in may possibly 2000. The 39 revised complete papers awarded have been rigorously chosen from a complete of one hundred fifty submissions in the course of a hugely aggressive reviewing approach. The booklet is split in topical sections of factoring and discrete logarithm, electronic signatures, deepest details retrieval, key administration protocols, threshold cryptography, public-key encryption, quantum cryptography, multi-party computation and data concept, zero-knowledge, symmetric cryptography, Boolean features and undefined, vote casting schemes, and circulate ciphers and block ciphers.

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Additional resources for Advances in Cryptology — EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques Bruges, Belgium, May 14–18, 2000 Proceedings

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Dependencies modulo 2 among the vectors are determined in the matrix processing step. How the matrix step is carried out is described in the literature referred to in [1]. 4 Arjen K. Lenstra and Adi Shamir Algebraic Square Root Computation Each dependency modulo 2 leads with probability at least one half to the factorization of n in the last step of the NFS. References describing how this is done can be found in [1]. 5 Sieving So far two distinct sieving methods have been used in NFS implementations: line sieving and special q sieving.

Operations in the matrix-vector multiplication and scalar products), we used direct calls to some assembly routines taken from the GMP [18] and BigNum [20] packages. Indeed our compact representation of the matrix led to an overcost when using the ZEN functions. We used a classical representation (we could probably obtain a better efficiency with Montgomery representation), with the lazy reduction technique explained in [8]. Before running Lanczos’s algorithm, a preprocessing can be done on the matrix (see [8] [5]).

1. Discrete log algorithm Some other optimizations can be done to speed up the computation. They will be described in section 5. 1 Analysis Probability for a Divisor to Be Smooth The following proposition gives the proportion of smooth divisors and then the probability of smoothness in a random walk. This is a key tool for the complexity analysis. An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves 25 Proposition 4 The proportion of smooth divisors in the Jacobian of a curve of genus over Fq tends to 1/ !

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Advances in Cryptology — EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques Bruges, Belgium, May 14–18, 2000 Proceedings by Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery (auth.), Bart Preneel (eds.)


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