ω-ary Bit-Elimination Algorithm for Extended GCD Problem : A Fast Method for Modular Reciprocal(<Special Issue>"Algorithmic Number Theory and Its Applications, Part 1")

Abstract

This paper presents a new algorithm for the extended integer GCD problem, which is often refered to for computing modular reciprocals, and has been being investigated rigorously. We apply the multi-bit elimination algorithm, recently developed for the integer GCD problem, to the extended problem. We show that the application cannot be straightforward, and there arise two problems related with exact division. To resolve these problems, we also apply the bit elimination algorithm. A brief discussion about implementation will be also given.