Comunicació presentada a: PKC 2009 12th International Conference on Practice and Theory in Public Key Cryptography, celebrada del 18 al 20 de març de 2009 a Irvine, Califòrnia, Estats Units d'Amèrica.

The relation between list decoding and hard-core predicates has provided a clean and easy methodology to prove the hardness of certain predicates. So far this methodology has only been used to prove that the O(log logN) least and most significant bits of any function with multiplicative access |which include the most common number theoretic trapdoor permutations| are secure. In this paper we show that the method applies to all bits of any function defined on a cyclic group of order N with multiplicative access for cryptographically interesting N. As a result, in this paper we reprove the security of all bits of RSA, the discrete logarithm in a group of prime order or the Paillier encryption scheme.