Relation Collection for the Function Field Sieve

In this paper, we focus on the relation collection step of the Function Field Sieve (FFS), which is to date the best algorithm known for computing discrete logarithms in small-characteristic finite fields of cryptographic sizes. Denoting such a finite field by F p n , where p is much smaller than n,...

Full description

Saved in:
Bibliographic Details
Main Authors: Detrey, J., Gaudry, P., Videau, M.
Format: Conference Proceeding
Language:English
Subjects:
Arrays
Cryptography
discrete logarithm
finite-field arithmetic
function field sieve
Lattices
polynomial arithmetic
Polynomials
Vectors
Citations: Items that cite this one
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we focus on the relation collection step of the Function Field Sieve (FFS), which is to date the best algorithm known for computing discrete logarithms in small-characteristic finite fields of cryptographic sizes. Denoting such a finite field by F p n , where p is much smaller than n, the main idea behind this step is to find polynomials of the form a(t)-b(t)x in F p [t][x] which, when considered as principal ideals in carefully selected function fields, can be factored into products of low-degree prime ideals. Such polynomials are called "relations", and current record-sized discrete-logarithm computations need billions of those. Collecting relations is therefore a crucial and extremely expensive step in FFS, and a practical implementation thereof requires heavy use of cache-aware sieving algorithms, along with efficient polynomial arithmetic over F p [t]. This paper presents the algorithmic and arithmetic techniques which were put together as part of a new public implementation of FFS, aimed at medium-to record-sized computations.
ISSN:1063-6889
DOI:10.1109/ARITH.2013.28