Institute of Electrical & Electronic Engineers
In this paper, the authors propose two improved interleaved modular multiplication algorithms based on Barrett and Montgomery modular reduction. The algorithms are simple and especially suitable for hardware implementations. Four large sets of moduli for which the proposed methods apply are given and analyzed from a security point of view. By considering state-of-the-art attacks on public-key cryptosystems, the authors show that the proposed sets are safe to use, in practice, for both elliptic curve cryptography and RSA cryptosystems. They propose hardware architecture for the modular multiplier that is based on their methods.