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 2 2ℓ had a complexity of (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. © 2011 International Association for Cryptologic Research.