High-Performance RAD-Based Interleaved Modular Multiplication for Elliptic Curve Cryptography Over GF(p)

This paper presents a novel interleaved modular multiplication (IMM) algorithm and its dedicated hardware architecture for elliptic curve cryptography (ECC) over a general prime field, aiming to overcome performance limitations of the conventional two-level radix-2 modular multiplication (MM) design. The proposed IMM algorithm is based on one-level redundant signed-digit (RSD) adders and incorporates a detecting-and-skipping mechanism to bypass unnecessary addition iterations. As a result, the proposed design achieves low hardware overhead and a shortened critical path delay. Compared with existing MM designs, the proposed architecture achieves a 1.05×-3.41× reduction in area-time product (ATP) over the 256-bit prime field. At the group-operation level, left-to-right signed-digit (X,Y)-only Co-Z arithmetic is adopted for scalar point multiplication (SPM). Implementation results demonstrate that the proposed SPM design achieves a 1.25×-3.59× reduction in ATP.