By Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery (auth.), Bart Preneel (eds.)
This e-book constitutes the refereed court cases of the foreign convention at the idea and alertness of Cryptographic recommendations, EUROCRYPT 2000, held in Bruges, Belgium, in might 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 procedure. The ebook 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 idea, zero-knowledge, symmetric cryptography, Boolean features and undefined, balloting schemes, and circulate ciphers and block ciphers.
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Extra resources for Advances in Cryptology — EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques Bruges, Belgium, May 14–18, 2000 Proceedings
The ﬁrst one deals with the building of the matrix and is written in the computer algebra system Magma , which is a very good compromise between high level programming and eﬃciency. The second part is our optimized implementation of the Lanczos algorithm written in C. 1 Pierrick Gaudry Implementation of the Search for Relations This part of the implementation was not optimized: it can be done in parallel and it is not the limiting phase. However an interesting optimization suggested by Fran¸cois Morain has been tested.
K. S. Manasse. Factoring with two large primes. B. D˚ amgard, editor, Advances in Cryptology – Eurocrypt ’90, volume 473 of Lecture Notes in Computer Science, pages 72–82, Springer-Verlag, Berlin, 1991. 23. Arjen K. Lenstra and Eric R. Verheul. Selecting Cryptographic Key Sizes. In H. Imai and Y. Zheng, editors, Public Key Cryptography, volume 1751 of Lecture Notes in Computer Science, pages 446–465, Springer-Verlag, Berlin, 2000. 24. Peter L. Montgomery. Square roots of products of algebraic numbers.
Thus, three large primes are allowed on the algebraic side, but only two large primes are allowed on the rational side. There are about one million primes < 224 , more precisely π(224 ) =1,077,871. 5. The sieving region is skew with skewness ratio s. The resulting candidate pairs are trial divided to inspect if they indeed lead to relations. How the sieving and the trial division may be carried out is addressed in the next section. It is the most time consuming step of the NFS, and it is the step for which we want to use the TWINKLE device.
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.)