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

This publication constitutes the refereed complaints of the overseas convention at the thought and alertness of Cryptographic recommendations, EUROCRYPT 2000, held in Bruges, Belgium, in may well 2000. The 39 revised complete papers offered have been rigorously chosen from a complete of a hundred and fifty submissions in the course of a hugely aggressive reviewing strategy. The ebook is split in topical sections of factoring and discrete logarithm, electronic signatures, inner most info retrieval, key administration protocols, threshold cryptography, public-key encryption, quantum cryptography, multi-party computation and knowledge thought, zero-knowledge, symmetric cryptography, Boolean services and undefined, vote casting schemes, and movement ciphers and block ciphers.

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Pollard. Monte Carlo methods for index computation mod p. Math. , 32(143):918–924, July 1978. 35. H. G. R¨ uck. On the discrete logarithm in the divisor class group of curves. Math. , 68(226):805–806, 1999. 36. Y. Sakai and K. Sakurai. Design of hyperelliptic cryptosystems in small charatcteristic and a software implementation over 2n . In K. Ohta and D. Pei, editors, Advances in Cryptology, volume 1514 of Lecture Notes in Comput. , pages 80– 94. Springer–Verlag, 1998. Proc. Asiacrypt ’98, Beijing, October, 1998.

Lenstra and Adi Shamir All PC running times referred to in this paper are actual measurements rather than asymptotic or conjectured running times. They are based on optimized implementations of the various algorithms on a 450MHz Pentium II PC with 192 megabytes of RAM. However, the TWINKLE device itself has not been built so far, and thus its feasibility, performance, and cost are open to debate. 2 The Original TWINKLE Design We recall the basics of the TWINKLE device as described in [7]. The most time consuming step of most modern factoring algorithm is the ‘sieving step’: for many pairs of integers (p, r) in succession add an approximation of log(p) to location r + kp of a sieve interval (initialized as zeros) for all integers k such that r + kp is in the interval, and report all j for which location j exceeds a certain threshold.

McCurley. A rigorous subexponential algorithm for computation of class groups. J. Amer. Math. , 2(4):837–850, 1989. 20. -C. Herv´e, B. Serpette, and J. Vuillemin. BigNum: A portable and efficient package for arbitrary-precision arithmetic. Technical Report 2, Digital Paris Research Laboratory, May 1989. 21. -D. Huang and D. Ierardi. Counting points on curves over finite fields. J. , 25:1–21, 1998. 22. T. Izu, J. Kogure, M. Noro, and K. Yokoyama. Efficient implementation of Schoof’s algorithm. In K. Ohta and D.

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