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 publication constitutes the refereed court cases of the overseas convention at the thought and alertness of Cryptographic concepts, EUROCRYPT 2000, held in Bruges, Belgium, in could 2000. The 39 revised complete papers provided have been rigorously chosen from a complete of one hundred fifty submissions in the course of a hugely aggressive reviewing method. The e-book is split in topical sections of factoring and discrete logarithm, electronic signatures, deepest info 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, balloting schemes, and circulation ciphers and block ciphers.

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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

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Finally, for all a such that gcd(a, b) = 1, S1 (a) > T1 , and S2 (a) > T2 inspect if both F1 (a, b) and F2 (a, b) are smooth. For a fixed b-value the a-interval −A ≤ a < A is referred to as a line. , per b-value. 3 41 Special Sieving For pairs (q, rq ) with f1 (rq ) ≡ 0 mod q, q prime, and 224 < q < 109 do the following. Let Lq be the lattice spanned by the two 2-dimensional vectors (q, 0)T and (rq , 1)T . , ‘small’ (a, b) pairs for which q divides F1 (a, b), is approximated as follows. Find a basis (x1 , y1 )T , (x2 , y2 )T for Lq for which |xi | ≈ |s ∗ yi |.

Springer–Verlag, 1990. Proc. Crypto ’90, Santa Barbara, August 11–15, 1988. ´ 28. R. Lercier. Algorithmique des courbes elliptiques dans les corps finis. Th`ese, Ecole polytechnique, June 1997. 29. R. Lercier and F. Morain. Counting the number of points on elliptic curves over finite fields: strategies and performances. In L. C. -J. Quisquater, editors, Advances in Cryptology – EUROCRYPT ’95, volume 921 of Lecture Notes in Comput. , pages 79–94, 1995. Saint-Malo, France, May 1995, Proceedings. 30.

Th`ese, Ecole polytechnique, June 1997. 29. R. Lercier and F. Morain. Counting the number of points on elliptic curves over finite fields: strategies and performances. In L. C. -J. Quisquater, editors, Advances in Cryptology – EUROCRYPT ’95, volume 921 of Lecture Notes in Comput. , pages 79–94, 1995. Saint-Malo, France, May 1995, Proceedings. 30. A. Menezes, T. Okamoto, and S. A. Vanstone. Reducing elliptic curves logarithms to logarithms in a finite field. IEEE Trans. Inform. Theory, 39(5):1639–1646, September 1993.

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