Selecting polynomials for the Function Field Sieve

Razvan Barbulescu

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arXiv · 1303.1998

Selecting polynomials for the Function Field Sieve

Razvan Barbulescu

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Abstract

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

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Razvan Barbulescu. 2013-03-08. Selecting polynomials for the Function Field Sieve. https://arxiv.org/abs/1303.1998

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