Abstract
In this paper, we re-examine the bit security of Paillier's trapdoor function. We show that given a random w = g c y N mod N 2 ∈ Z N2 * the most significant bit of its class c is a hard-core predicate, under a standard assumption that is computing composite residuosity class is hard. For the simultaneous security, we prove that n number of the class c 's bits are simultaneously hard-core under the standard assumption, where n is the length of c .
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