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| HAL: inria-00337753, version 2 |
| DOI: 10.1007/978-3-642-10868-6_21 |
| See detailed view |  BibTeX,EndNote,... |
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| Twelfth IMA International Conference on Cryptography and Coding, Cirencester : Royaume-Uni (2009) |
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| Available versions | v1 (2008-11-08) | v2 (2009-11-18) |
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| Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms |
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| Antoine Joux 1Reynald Lercier 2 |
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| (2009) |
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| This paper extends Joux-Naccache-Thomé's e-th root algorithm to the static Diffie-Hellman problem (sdhp). The new algorithm can be adapted to diverse finite fields by customizing it with an nfs-like core or an ffs-like core. In both cases, after a number of sdhp oracle queries, the attacker builds-up the ability to solve new sdhp instances unknown before the query phase. While sub-exponential, the algorithm is still significantly faster than all currently known dlp and sdhp resolution methods. We explore the applicability of the technique to various cryptosystems. The attacks were implemented in F_{2^1025} and also in F_p, for a 516-bit p. |
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| 1: | Parallélisme, Réseaux, Systèmes d'information, Modélisation (PRISM) |
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CNRS : UMR8144 – Université de Versailles Saint-Quentin-en-Yvelines |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3: | Laboratoire d'informatique de l'école normale supérieure (LIENS) |
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CNRS : UMR8548 – Ecole normale supérieure de Paris - ENS Paris |
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| 4: | CACAO (INRIA Lorraine - LORIA) |
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CNRS : UMR7503 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| Domain | : | Computer Science/Cryptography and Security |
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| Discrete logarithm problem – Static Diffie-Hellman problem – Function Field Sieve – Number Field Sieve |
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| inria-00337753, version 2 | |
| http://hal.inria.fr/inria-00337753 | |
| oai:hal.inria.fr:inria-00337753 | |
| From: Emmanuel Thomé | |
| Submitted on: Tuesday, 17 November 2009 22:52:01 | |
| Updated on: Tuesday, 23 March 2010 13:35:58 | |
