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Relation collection for the Function Field Sieve
Abstract : In this paper, we focus on the relation collection step of the Function Field Sieve (FFS), which is to date the best known algorithm for computing discrete logarithms in small-characteristic finite fields of cryptographic sizes. Denoting such a finite field by GF(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 GF(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 require billions of them. 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 GF(p)[t]. This paper presents the algorithmic and arithmetic techniques which were put together as part of a new implementation of FFS, aimed at medium- to record-sized computations, and planned for public release in the near future.
Cited literature [21 references]
https://hal.inria.fr/hal-00736123
Contributor : Pierrick Gaudry Connect in order to contact the contributor
Submitted on : Friday, January 18, 2013 - 2:01:58 PM
Last modification on : Wednesday, February 2, 2022 - 3:59:45 PM
Long-term archiving on: : Saturday, April 1, 2017 - 7:04:23 AM
Contributor : Pierrick Gaudry Connect in order to contact the contributor
Submitted on : Friday, January 18, 2013 - 2:01:58 PM
Last modification on : Wednesday, February 2, 2022 - 3:59:45 PM
Long-term archiving on: : Saturday, April 1, 2017 - 7:04:23 AM
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