Titlebook: Algorithmic Number Theory; 4th International Sy Wieb Bosma Conference proceedings 2000 Springer-Verlag Berlin Heidelberg 2000 Algorithmic N

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Curves over Finite Fields with Many Rational Points Obtained by Ray Class Field Extensionsegrees of these extensions, which turns out to be the main difficulty. While in two special situations explicit formulas for the degrees are known, the general problem is solved algorithmically. The systematic application of the methods described yields several new examples of algebraic curves over

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Baby-Step Giant-Step Algorithms for Non-uniform Distributionsalisation of this algorithm, where extra baby steps may be computed after carrying out giant steps (thus increasing the giant step size). The paper considers the problem of deciding how many, and when, extra baby steps should be computed so that the expected cost of the generalised algorithm is mini

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Strategies in Filtering in the Number Field Sieve using a Block Lanczos algorithm. Both size and weight (the number of non-zero elements) of the matrix critically affect the running time of Block Lanczos. In order to keep size and weight small the relations coming out of the siever do not flow directly into the matrix, but are filtered first in or