Discrete logarithms in GF(2^n) From: Reynald LERCIER <[email protected]> To: [email protected] Date: Tue, 25 Sep 2001 13:37:18 -0400 We are pleased to announce a new record for the discrete logarithm problem. We were able to compute discrete logarithms in GF(2^521). This was done in one month on a unique 525MHz quadri-processors Digital Alpha Server 8400 computer. The approach that we followed is a careful implementation of the general Function Field Sieve as described from a theoretical point of view by Adleman [Ad94]. As far as we know, the largest such computation previously done was performed in GF(2^401) [GoMc92] using an algorithm due to Coppersmith [Co84]. [...] So, as a conclusion, time that we need for computing discrete logarithms in GF(2^521) on a 525 MHz quadri-processor alpha server 8400 computer is approximatively 12 hours for each, once the sieving step (21 days) and the linear algebra step (10 days) is performed. Antoine JOUX (DCSSI, Issy les Moulineaux, France, [email protected]), Reynald LERCIER (CELAR, Rennes, France, [email protected]).