Abstract:In this short note, we show that substantially weaker Low Order assumptions are sufficient to prove the soundness of Pietrzak's protocol for proof of exponentiation in groups of unknown order. This constitutes the first step to a better understanding of the asymptotic computational complexity of breaking the soundness of the protocol. Furthermore, we prove the equivalence of the (weaker) Low Order assumption(s) and the Factoring assumption in RSA groups for a non-negligible portion of moduli. We argue that in … Show more
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