Titlebook: Algorithmic Number Theory; 6th International Sy Duncan Buell Conference proceedings 2004 Springer-Verlag Berlin Heidelberg 2004 Farey seque

GRIPE

Proving the Primality of Very Large Numbers with fastECPPion, fastECPP, runs in heuristic time .. The aim of this article is to describe new ideas used when dealing with very large numbers. We illustrate these with the primality proofs of some numbers with more than 10,000 decimal digits.

enhance

A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii’s Algorithmgorithm computes the group order of the Jacobian of a genus 2 curve over a finite field for which the characteristic polynomial of the Frobenius endomorphism is known modulo some integer. The main tool is a 2-dimensional pseudo-random walk that allows to heuristically choose random elements in a 2-d

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