Cryptanalysis of the RSA Subgroup Assumption from TCC 2005
- Cite this paper as:
- Coron JS., Joux A., Mandal A., Naccache D., Tibouchi M. (2011) Cryptanalysis of the RSA Subgroup Assumption from TCC 2005. In: Catalano D., Fazio N., Gennaro R., Nicolosi A. (eds) Public Key Cryptography – PKC 2011. PKC 2011. Lecture Notes in Computer Science, vol 6571. Springer, Berlin, Heidelberg
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.