Paper 2013/197

Discrete logarithm in GF(2^809) with FFS

Razvan Barbulescu and Cyril Bouvier and Jérémie Detrey and Pierrick Gaudry and Hamza Jeljeli and Emmanuel Thomé and Marion Videau and Paul Zimmermann

Abstract

We give details on solving the discrete logarithm problem in the 202-bit prime order subgroup of $GF(2^{809})^\times$ using the Function Field Sieve algorithm (FFS). To our knowledge, this computation is the largest discrete logarithm computation so far in a binary field extension of prime degree. The Function Field Sieve is the traditional approach for solving these problems, and has been used in previous records for such fields, namely GF(2^{619}) and GF(2^{613}).