Cryptology ePrint Archive: Report 2014/419

FFS Factory: Adapting Coppersmith's "Factorization Factory" to the Function Field Sieve

J\'er\'emie 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.

Category / Keywords: public-key cryptography / Discrete logarithm, Function field sieve, Cryptanalysis

Date: received 3 Jun 2014

Contact author: Jeremie Detrey at loria fr

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Version: 20140605:203918 (All versions of this report)

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