Fraction-Integer Method (FIM): Calculating Multiplicative Inverse

Multiplicative inverse is a crucial operation in cryptographic systems; public key cryptography has given rise to such a need [6], in which we need to generate a related public/private pair of numbers, each of which is the inverse of the other. One of the best methods for calculating the multiplicative inverse is Extended-Euclidean method. In this paper we will propose a new algorithm for calculating the inverse, based on continuous adding of two fraction numbers until an integer is obtained.