The geometry of provable security: Some proofs of security in which lattices make a surprise appearance

Abstract

We highlight some uses of lattice reduction in security proofs of nonlattice-based cryptosystems. In particular, we focus on RSA-OAEP, the Rabin partial-domain hash signature scheme, techniques to compress Rabin signatures and ciphertexts, the relationship between the RSA and Paillier problems and Hensel lifting, and the hardness of the most significant bits of a Diffie–Hellman secret.