Counting points in medium characteristic using Kedlaya's algorithm.
Integer factorization and discrete logarithm problems
These are notes for a lecture given at CIRM in 2014, for the “Journées Nationales du Calcul Formel”. We explain the basic algorithms based on combining congruences for solving the integer factorization and the discrete logarithm problems. We highlight two particular situations where the interaction with symbolic computation is visible: the use of Gröbner basis in Joux’s algorithm for discrete logarithm in finite field of small characteristic, and the exact sparse linear algebra tools that occur...
A general framework for subexponential discrete logarithm algorithms
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