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Title:
Cryptanalysis of the RSA Subgroup Assumption from TCC 2005
Authors: Jean-Sebastien Coron, Antoine Joux, Avradip Mandal, David Naccache, Mehdi Tibouchi
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 2^{2k} had a complexity of O{2^k}. Accordingly, k=100 bits was suggested as a concrete parameter. This paper exhibits an attack with a complexity of roughly 2^{k/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.
ePrint: https://eprint.iacr.org/2010/650
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