Welcome to the resource topic for 2008/217
Title:
Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms
Authors: Antoine Joux, Reynald Lercier, David Naccache, Emmanuel Thomé
Abstract:This paper extends Joux-Naccache-Thomé’s e-th root algorithm to the static Diffie-Hellman problem ({\sc sdhp}). The new algorithm can be adapted to diverse finite fields by customizing it with an {\sc nfs}-like core or an {\sc ffs}-like core. In both cases, after a number of {\sc sdhp} oracle queries, the attacker builds-up the ability to solve new {\sc sdhp} instances {\sl unknown before the query phase}. While sub-exponential, the algorithm is still significantly faster than all currently known {\sc dlp} and {\sc sdhp} resolution methods. We explore the applicability of the technique to various cryptosystems. The attacks were implemented in {\mathbb F}_{2^{1025}} and also in {\mathbb F}_{p}, for a 516-bit p.
ePrint: https://eprint.iacr.org/2008/217
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