Fast Fraction-Integer Method for Computing Multiplicative Inverse

TL;DR

This paper introduces a new, more efficient algorithm for computing multiplicative inverses in cryptography, based on continued fraction techniques, promising faster performance than traditional methods.

Contribution

The paper proposes a novel algorithm utilizing continued fractions for faster computation of multiplicative inverses, improving efficiency over existing methods.

Findings

The new method is more efficient than Extended-Euclidean algorithm.

It reduces computational time for large integers.

Experimental results show improved speed in inverse calculation.

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.