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Journals ACM Communications in Computer Algebra Volume 42 Issue 1-2

ANTS-8 Poster Abstracts For i = 1 to n Do ai = c . ai+1 + (1 ’ c) . ai EndFor Return A = (an , an ’1 , , a1 ). The For version of the GCD algorithm is clearly a straight-line program using only the ring operations +, ’, and × on bits with O(n4 ) steps, however the degree of the polynomials generated by the program is exponential. References [1] B. Chor and O. Goldreich, An improved parallel algorithm for integer GCD, Algorithmica. 5 (1990). [2] S. Cook, A Taxonomy of Problems with Fast Parallel Algorithms, Information and Control. 64 (1985) 2 “22. [3] M.S. Sedjelmaci, On a Parallel Lehmer-Euclid GCD Algorithm, Proceedings of the International Symposium on Symbolic and Algebraic Computation ISSAC ™2001 (2001) 303 “308. [4] J. Sorenson, Two Fast GCD Algorithms, J. of Algorithms 16 (1994) 110 “144. [5] L.G. Valiant, S. Skyum, S. Berkowitz and C. Racko €, Fast parallel computation of polynomials using few processors, SIAM J.Computing 12 No.4 (1983) 641 “644. The discrete logarithm problem on elliptic curves de ned over Q Masaya Yasuda, Fujitsu Laboratories Ltd., myasuda@labs.fujitsu.com The discrete logarithm problem on elliptic curves de ned over

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The discrete logarithm problem on elliptic curves defined over Q (abstract only)

Yasuda, Masaya
ACM Communications in Computer Algebra , Volume 42 (1-2)
Association for Computing Machinery – Jul 25, 2008

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