2013/03/08 by Razvan Barbulescu, Barbulescu, Razvan
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1303.1998
openalex publication_date 2013/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Function Field Sieve algorithm is dedicated to computing discrete logarithms in a finite field GF(qn), 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.