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

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

This e-book constitutes the refereed lawsuits of the foreign convention at the idea and alertness of Cryptographic ideas, EUROCRYPT 2000, held in Bruges, Belgium, in may perhaps 2000. The 39 revised complete papers offered have been conscientiously chosen from a complete of a hundred and fifty submissions in the course of a hugely aggressive reviewing approach. The ebook 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, vote casting schemes, and circulate ciphers and block ciphers.

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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

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To demonstrate the efficiency of our approach, we describe our breaking of a cryptosystem based on a curve of genus 6 recently proposed by Koblitz. 1 Introduction The use of hyperelliptic curves in public-key cryptography was first proposed by Koblitz in 1989 [24]. It appears as an alternative to the use of elliptic curves [23] [31], with the advantage that it uses a smaller base field for the same level of security. Several authors have given ways to build hyperelliptic cryptosystems efficiently. The security of such systems relies on the difficulty of solving the discrete logarithm problem in the Jacobian of hyperelliptic curves.

The main purpose of this paper is to carry out a detailed and realistic analysis of the expected behavior of a TWINKLEassisted factoring attempt on inputs whose binary sizes are 384, 512, and 768 bits. In particular, we describe the optimal choice of the many parameters involved in such factoring attempts, and identify several areas in which the original TWINKLE design leads to computational bottlenecks. We then propose enhanced hardware and algorithmic designs which eliminate these bottlenecks, and make such factorizations more feasible.

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. The following table gives precise information on that curve. field F5026243 2 equation + = 13 genus 6 #J 133 × 7345240503856807663632202049344834001 ≈ 1040 We give the measured timings for the computation of a discrete logarithm in the following table. These timings are on a Pentium II 450 MHz with 128 Mb. During the Lanczos’s step (the most space consuming part of the algorithm), the memory used was around 60Mb.

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