Fast Fraction-Integer Method for Computing Multiplicative Inverse

Abstract - Multiplicative inverse is a crucial operation in public key cryptography, and been widely used in cryptography. Public key cryptography has given rise to such a need, in which we need to generate a related public and private pair of numbers, each of which is the inverse of the other. The basic method to find multiplicative inverses is Extended-Euclidean method. In this paper we will propose a new algorithm for computing the inverse, based on continues subtract fraction from integer and divide by fraction to obtain integer that will be used to compute the inverse d. The authors claim that the proposed method more efficient and faster than the existed methods. Keywords - Multiplicative inverse, greater common divisor, Euclidean method, Stein method, Gordon method, Baghdad method 1. Introduction Modular arithmetic plays an important role in cryptography. Many public-key schemes [2] involve modular exponentiation. Modular inversion, the computation of b −1 mod a has a part in exponentiation based on addition-subtraction chains [6], as well as other applications in such public key systems. The multiplicative inverse of