A radix-4 scalable design

Modular arithmetic operations are very important in cryptography. Modular multiplication is the most common arithmetic operation used in many cryptographic algorithms such as the Elliptic Curve Cryptography and the Diffie-Helman key exchange. The Montgomery Modular Multiplication algorithm (MM) has permitted cryptographic algorithms to speed up considerably. Multiplication is implemented by a series of multiprecision partial-product addition. The proposed multiple-word Radix-4 Montgomery Multiplication algorithm (R4MM) is extension of the Multiple-Word High-Radix (R2^k) Montgomery Multiplication algorithm (MWR2^kMM). There are two types of recoding applied in the R4MM. The architecture of the modular multiplier that implements the R4MM consists of three main blocks: the datapath (or kernel), the IO & memory and the control block. The computation in the R4MM algorithm takes place in the kernel. We show that a more elaborate design using two types of digit recoding makes the radix-4 design the best solution for the implementation of this scalable multiplier.