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OPAKE: Security Theorem d = size of dictionary n = number of online authentication attempts t = running time of adversary AdvHSS = probability of finding a “hidden smooth subgroup” AdvOPAKE = advantage in breaking OPAKE AdvOPAKE(t) = n/d + AdvHSS(O(t)) + e Interpretation If hidden smooth subgroup problem is hard, then in OPAKE the adversary has negligible advantage over a simple online dictionary attack |