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Discrete logarithm in GF($2^{809}$) with FFS

Razvan Barbulescu 1 Cyril Bouvier 1 Jérémie Detrey 1 Pierrick Gaudry 1 Hamza Jeljeli 1 Emmanuel Thomé 1 Marion Videau 1 Paul Zimmermann 1 
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : The year 2013 has seen several major complexity advances for the discrete logarithm problem in multiplicative groups of small- characteristic finite fields. These outmatch, asymptotically, the Function Field Sieve (FFS) approach, which was so far the most efficient algorithm known for this task. Yet, on the practical side, it is not clear whether the new algorithms are uniformly better than FFS. This article presents the state of the art with regard to the FFS algorithm, and reports data from a record-sized discrete logarithm computation in a prime-degree extension field.
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Submitted on : Saturday, November 9, 2013 - 11:43:23 AM
Last modification on : Saturday, June 25, 2022 - 7:43:07 PM
Long-term archiving on: : Friday, April 7, 2017 - 11:08:19 PM


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Razvan Barbulescu, Cyril Bouvier, Jérémie Detrey, Pierrick Gaudry, Hamza Jeljeli, et al.. Discrete logarithm in GF($2^{809}$) with FFS. Public-Key Cryptography – PKC 2014, 2014, Buenos Aires, Argentina. ⟨10.1007/978-3-642-54631-0_13⟩. ⟨hal-00818124v3⟩



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