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UID:8142@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150312T110000
DTEND;TZID=Europe/Paris:20150312T120000
DTSTAMP:20241120T210042Z
URL:https://www.i2m.univ-amu.fr/evenements/polynomial-selection-for-nfs-dl
 -in-finite-fields-gf-p-k-of-medium-to-large-characteristic-with-practical-
 application-to-gf-p-2/
SUMMARY:Aurore Guillevic (...): Polynomial selection for NFS-DL in finite f
 ields GF(p^k) of medium to large characteristic with practical application
  to GF(p^2)
DESCRIPTION:Aurore Guillevic: This talk is about the asymptotic and practic
 al hardness of discrete logarithms (DL) in non-prime finite fields of medi
 um to large characteristic. This is needed to evaluate the security of e.g
 . pairing-based cryptosystems. The Number Field Sieve (NFS) algorithm is k
 nown to be the most efficient to compute discrete logarithms in prime fini
 te fields and large characteristic finite fields. We are interested in ada
 pting NFS for DL in GF(p^k)\, starting with k=2. NFS algorithm requires tw
 o number fields that can be embedded into GF(p^k). We introduce two new me
 thods for polynomial selection\, i.e. the choice of the two polynomials de
 fining the two number fields involved in NFS. We generalize the Joux-Lerci
 er method\, and propose the Conjugation method.\nThese methods provide an 
 important practical speed-up for DL in GF(p^2) compared to DL in prime fie
 lds of the same size. We show that by a record of DL computation in a fiel
 d GF(p^2) of 180 decimal digits (p is 90 digit long).\n\nOur methods have 
 an asymptotic complexity of L(1/3\,(64/9)^(1/3)). Moreover they can be app
 lied in medium-sized characteristic and have in this case a better asympto
 tic complexity of L(1/3\, (96/9)^(1/3)) instead of L(1/3\, (128/9)^(1/3)).
  Compared to the recent MNFS paper\, our asymtotic complexity is slightly 
 better (2.20 vs 2.24 for the second constant in the L(1/3) formula).\n\nTh
 is is a joint work with Razvan Barbulescu\, Pierrick Gaudry and François 
 Morain from the CATREL project (http://catrel.loria.fr).\n\nAurore Guillev
 ic\, Inria Nancy Grand Est\, Équipe CARAMBA \n\n
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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