Abstract

AbstractAt EuroCrypt ’01, Catalano et al. [1] proved that for Paillier’s trapdoor function if computing residuosity class is hard, then given a random \(w\in\mathbb{Z}_{N^2}^*\) the least significant bit of its class is a hard-core predicate. In this paper, we reconsider the bit security of Paillier’s trapdoor function and show that under the same assumption, the most significant bit of the class of w is also a hard-core predicate. In our proof, we use the ”guessing and trimming” technique [2] to find a polynomial number of possible values of the class and devise a result checking method to test the validity of them.KeywordsPaillier’s trapdoor functionHard-core PredicateMost significant bit

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