New Algorithm for Classical Modular Inverse

Abstract

The Montgomery inverse is used in cryptography for the computation of modular inverse of 6 modulo a, where a is a prime. We analyse existing algorithms from the point of view of their hardware implementation. We propose a new, hardware-optimal algorithm for the calculation of the classical modular inverse. The left-shift binary algorithm is shown to naturally calculate the classical modular inverse in fewer operations than the algorithm derived from the Montgomery inverse. © Springer-Verlag 2003.