Efficient modular exponential algorithms compatible with hardware implementation of public-key cryptography

Abstract

It is widely recognized that the public-key cryptosystem is playing a pivotal role to provide the security services not only in electronic world but also for secured key exchanges in military applications. Modular exponentiation is the crucial, but expensive, operation in several public-key cryptostyems, which makes use of repeated modular multiplications. So, the performance of public-key cryptography is highly influenced by the competent implementation of modular exponentiation. In order to speed up the entire process, it is essential to develop the modular exponential algorithms, which reduces the frequency of modular multiplications, and the time required to implement each modular multiplication. In this paper, we present the bit forwarding BFW techniques to reduce the count of modular multiplications for hardware implementation of modular exponentiation. Montgomery multiplication method is customized according to the needs of BFW techniques and implemented with radix-2, named as adaptable Montgomery multiplication, and also implemented with high radix and named as adaptable high-radix Montgomery multiplication. It has been computed that it is possible to reduce 11.16%, 15.14% and 18.20% of modular multiplications by BFW1, BFW2, and BFW3 algorithms, respectively, for 1024-bit exponent in comparison with prevailing techniques. This reduction will result in increased throughput and decreased power consumption. Copyright © 2016 John Wiley & Sons, Ltd.