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| HAL : hal-00714340, version 1 |
| DOI : 10.1007/s10958-009-9403-5 |
| Fiche détaillée |  Récupérer au format |
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| Journal of Mathematical Sciences 158, 5 (2009) 633-644 |
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| Time hierarchies for cryptographic function inversion with nonuniform advice |
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| Dima Grigoriev 1 |
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| (2009) |
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| We prove a time hierarchy theorem for inverting functions computable in a slightly nonuniform polynomial time. In particular, we prove that if there is a strongly one-way function, then for any k and for any polynomial p, there is a function f computable in linear time with one bit of advice such that there is a polynomial-time probabilistic adversary that inverts f with probability ≥ 1/p(n) on infinitely many lengths of input, while all probabilistic O(n k )-time adversaries with logarithmic advice invert f with probability less than 1/p(n) on almost all lengths of input. We also prove a similar theorem in the worst-case setting, i.e., if P ≠ NP, then for every l > k ≥ 1 |
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| 1 : | 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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| Géométrie algébrique réelle |
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| hal-00714340, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00714340 | |
| oai:hal.archives-ouvertes.fr:hal-00714340 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Mercredi 4 Juillet 2012, 10:04:23 | |
| Dernière modification le : Mercredi 4 Juillet 2012, 10:04:23 | |
