Selecting polynomials for the Function Field Sieve Article Swipe

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Mathematics Finite field Logarithm Field (mathematics) Function (biology) Sieve (category theory) Function field Prime (order theory) Discrete mathematics Discrete orthogonal polynomials Set (abstract data type) Orthogonal polynomials Algorithm Pure mathematics Combinatorics Mathematical analysis Computer science Evolutionary biology Biology Programming language

Razvan Barbulescu ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.1090/s0025-5718-2015-02940-8 · OA: W2020009028

The Function Field Sieve algorithm is dedicated to computing discrete\nlogarithms in a finite field GF(q^n), where q is small an prime power. The\nscope of this article is to select good polynomials for this algorithm by\ndefining and measuring the size property and the so-called root and\ncancellation properties. In particular we present an algorithm for rapidly\ntesting a large set of polynomials. Our study also explains the behaviour of\ninseparable polynomials, in particular we give an easy way to see that the\nalgorithm encompass the Coppersmith algorithm as a particular case.\n