A high speed redundant-signed-digit based montgomery modular multiplier

Abstract

Modular multiplication is the most crucial operation in the cryptographic systems that are based on the public key cryptography. In this work, a new architecture for radix-2 Montgomery Modular Multiplier (MMM) is proposed. The proposed design utilizes Redundant-Signed-Digit (RSD) arithmetic to optimize the critical path at the arithmetic level. The incorporation of the RSD arithmetic has significantly reduced the critical path of the proposed MMM. However, RSD arithmetic increases the area of the MMM. In order to compensate the increase in area, a new architecture for MMM is proposed that is based on a single adder instead of two as required in conventional MMM. The proposed design is implemented on Virtex-6 platform for various field sizes. It can perform a 256 bit modular multiplication in 0.73us and utilizes 3.8k Look-Up Tables. The proposed design achieves higher speed than other counterparts and occupies competitive area.