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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...
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