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Conference Papers Year : 2011

Cryptanalysis of the RSA Subgroup Assumption from TCC 2005

Abstract

At TCC 2005, Groth underlined the usefulness of working in small RSA subgroups of hidden order. In assessing the security of the relevant hard problems, however, the best attack considered for a subgroup of size 22ℓ had a complexity of O(2ℓ). Accordingly, ℓ= 100 bits was suggested as a concrete parameter. This paper exhibits an attack with a complexity of roughly 2ℓ/2 operations, suggesting that Groth’s original choice of parameters was overly aggressive. It also discusses the practicality of this new attack and various implementation issues.

Dates and versions

hal-01110234 , version 1 (27-01-2015)

Identifiers

Cite

Jean-Sébastien Coron, Antoine Joux, Avradip Mandal, David Naccache, Mehdi Tibouchi. Cryptanalysis of the RSA Subgroup Assumption from TCC 2005. PKC 2011 - Proceedings of the 2011 International Conference on Practice and Theory in Public Key Cryptography, Mar 2011, Taormina, Italy. pp.147-155, ⟨10.1007/978-3-642-19379-8_9⟩. ⟨hal-01110234⟩
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