Advances in Cryptology — EUROCRYPT 2000: International by Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter

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

This ebook constitutes the refereed lawsuits of the overseas convention at the concept and alertness of Cryptographic concepts, EUROCRYPT 2000, held in Bruges, Belgium, in may well 2000. The 39 revised complete papers provided have been conscientiously chosen from a complete of a hundred and fifty submissions in the course of a hugely aggressive reviewing approach. The publication is split in topical sections of factoring and discrete logarithm, electronic signatures, inner most details retrieval, key administration protocols, threshold cryptography, public-key encryption, quantum cryptography, multi-party computation and data thought, zero-knowledge, symmetric cryptography, Boolean features and undefined, balloting schemes, and move ciphers and block ciphers.

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

This ebook constitutes the refereed lawsuits of the overseas convention at the concept and alertness of Cryptographic concepts, EUROCRYPT 2000, held in Bruges, Belgium, in may well 2000. The 39 revised complete papers provided have been conscientiously chosen from a complete of a hundred and fifty submissions in the course of a hugely aggressive reviewing approach. The publication is split in topical sections of factoring and discrete logarithm, electronic signatures, inner most details retrieval, key administration protocols, threshold cryptography, public-key encryption, quantum cryptography, multi-party computation and data thought, zero-knowledge, symmetric cryptography, Boolean features and undefined, balloting schemes, and move ciphers and block ciphers.

Show description

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

Example text

We refer to [27] for a precise comparison of these two algorithms. e. e. 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].

26 Pierrick Gaudry Step 5. This last step requires only O ( ) multiplications modulo n, and one inversion. Hence the complexity is O ( n ). Finally, the overall complexity of the algorithm is O ( ! J )+O (( ! + 2 )( n + q,g )) + O ( q ). Now, by Cantor’s algorithm J is polynomial in log , and classical algorithm on finite fields and polynomials give n polynomial in n = log , q polynomial in log and q,g polynomial in log . Hence all these operations can be done in time bounded by a polynomial in log .

C Springer-Verlag Berlin Heidelberg 2000 20 Pierrick Gaudry the consequences for cryptographical applications is not clear. Enge [11] improved the original algorithm and gave a precise evaluation of the running time, but did not implement his ideas. M¨ uller, Stein and Thiel [32] extended the results to the real quadratic congruence function fields. Smart and Galbraith [16] also gave some ideas in the context of the Weil descent, following ideas of Frey; they dealt with general curves (not hyperelliptic).

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