By Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery (auth.), Bart Preneel (eds.)
This e-book constitutes the refereed complaints of the foreign convention at the conception and alertness of Cryptographic suggestions, EUROCRYPT 2000, held in Bruges, Belgium, in may well 2000. The 39 revised complete papers offered have been rigorously chosen from a complete of one hundred fifty submissions in the course of a hugely aggressive reviewing technique. 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 concept, zero-knowledge, symmetric cryptography, Boolean features and undefined, balloting schemes, and circulation ciphers and block ciphers.
Read Online or Download Advances in Cryptology — EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques Bruges, Belgium, May 14–18, 2000 Proceedings PDF
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Additional info for Advances in Cryptology — EUROCRYPT 2000: International Conference on the Theory and Application of Cryptographic Techniques Bruges, Belgium, May 14–18, 2000 Proceedings
For the examples below, we have run only the ﬁrst three tasks, our implementation of the last one being unsatisfactory. Therefore there is still some place for further optimizations. 3 Timings for Real Life Curves The ﬁrst example is a cryptosystem recently proposed by Buhler and Koblitz . e. we have worked on the curve 2 + = 13 , with a prime base ﬁeld of order greater than 5 000 000, with ≡ 1 mod 13. This curve has an automorphism of order 13 coming from complex multiplication, which helps in the computation of the order of the Jacobian, but helps also our attack.
B. The ﬁnal splitting of the polynomial in order to express the divisor on the factor basis can not be proved to be deterministic polynomial (though it is very fast in practice). For the analysis, we can then suppose that we do a trial division with all the elements of the basis. This leads to a complexity of O ( q,g ). Hence the complexity of step 3. ( J + n + q,g )) + O ( 2 q,g ). Step 4. This linear algebra step consists in ﬁnding a vector of the kernel in a sparse matrix of size O ( ), and of weight O ( ); the coeﬃcient are in Z/nZ.
Flassenberg and S. Paulus. Sieving in function ﬁelds. gz, 1997. 14. G. -G. R¨ uck. A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Math. , 62(206):865–874, April 1994. 15. W. Fulton. Algebraic curves. Math. Lec. Note Series. W. A. Benjamin Inc, 1969. 16. S. D. Galbraith and N. Smart. A cryptographic application of Weil descent. , 1999. 17. R. Gallant, R. Lambert, and S. Vanstone. Improving the parallelized Pollard lambda search on binary anomalous curves.