Paper 2014/419
FFS Factory: Adapting Coppersmith's "Factorization Factory" to the Function Field Sieve
Jérémie Detrey
Abstract
In 1993, Coppersmith introduced the "factorization factory" approach as a means to speed up the Number Field Sieve algorithm (NFS) when factoring batches of integers of similar size: at the expense of a large precomputation whose cost is amortized when considering sufficiently many integers to factor, the complexity of each individual factorization can then be lowered. We suggest here to extend this idea to the computation of discrete logarithms in finite fields of small characteristic using the Function Field Sieve (FFS), thus referring to this approach as the "FFS factory". In this paper, the benefits of the proposed technique are established thanks to both a theoretical complexity analysis along with a practical experiment in which we solved the discrete logarithm problem in fifty different binary fields of sizes ranging from 601 to 699 bits.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Discrete logarithmFunction field sieveCryptanalysis
- Contact author(s)
- Jeremie Detrey @ loria fr
- History
- 2014-06-05: received
- Short URL
- https://ia.cr/2014/419
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2014/419,
author = {Jérémie Detrey},
title = {{FFS} Factory: Adapting Coppersmith's "Factorization Factory" to the Function Field Sieve},
howpublished = {Cryptology {ePrint} Archive, Paper 2014/419},
year = {2014},
url = {https://eprint.iacr.org/2014/419}
}
