The RSA Group is Pseudo-Free
Identifieur interne : 000096 ( Main/Exploration ); précédent : 000095; suivant : 000097The RSA Group is Pseudo-Free
Auteurs : Daniele Micciancio [États-Unis]Source :
- Journal of Cryptology [ 0933-2790 ] ; 2010-04-01.
English descriptors
Abstract
Abstract: We prove, under the strong RSA assumption, that the group of invertible integers modulo the product of two safe primes is pseudo-free. More specifically, no polynomial-time algorithm can output (with non negligible probability) an unsatisfiable system of equations over the free Abelian group generated by the symbols g 1,…,g n, together with a solution modulo the product of two randomly chosen safe primes when g 1,…,g n are instantiated to randomly chosen quadratic residues. Ours is the first provably secure construction of pseudo-free Abelian groups under a standard cryptographic assumption and resolves a conjecture of Rivest (Theory of Cryptography Conference—Proceedings of TCC 2004, LNCS, vol. 2951, pp. 505–521, 2004).
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DOI: 10.1007/s00145-009-9042-5
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