Abstract: Montgomery Modular Multiplication is a method for performing fast modular multiplication. Modular multiplication is important in modern cryptography, as it is the basic operation that needs to be performed in many public key cryptosystems such as RSA. Rivest, Shamir, Adleman (RSA) algorithm can be used in cryptography to send confidential messages in secure manner. RSA cryptosystem is based on modular multiplication to factorize the large integers. Montgomery modular multiplication can be used as modular multiplication because it is one of the efficient and fastest modular multiplication. Montgomery algorithm is based on add and shift operation. Hardware is described for implementing the fast modular multiplication algorithm of P. L. Montgomery. The Karatsuba-Ofman multiplier replaces a multiplication by three ones of half-length operands which are performed in parallel. Large integer multiplication is the critical operation to design a modular multiplier. Karatsuba algorithm(KO algorithm) to split the operands into two parts is generally used to design a large integer multiplier. The most latest approach of Montgomery modular multiplication using KO algorithm, with which hardware resources can be reduced. Compared with other designs, the proposed design shows a better performance in terms of delay, area and power, and there is a significant improvement in latency and trade-off between area and performance.

Keywords: Montgomery modular multiplier, Large integer multiplication, Karatsuba algorithm.

| DOI: 10.17148/IJIREEICE.2021.9424