New modular multiplication and division algorithms based on continued fraction expansion

TL;DR

This paper introduces new algorithms for modular multiplication and division utilizing continued fraction expansions, based on the Euclidean algorithm, offering quadratic complexity solutions for modular arithmetic operations.

Contribution

The paper presents novel algorithms for modular multiplication and division that leverage continued fraction expansions, enhancing computational methods in modular arithmetic.

Findings

Algorithms are based on the Euclidean algorithm.

Both algorithms have quadratic complexity.

They improve computational efficiency in modular arithmetic.

Abstract

In this paper, we apply results on number systems based on continued fraction expansions to modular arithmetic. We provide two new algorithms in order to compute modular multiplication and modular division. The presented algorithms are based on the Euclidean algorithm and are of quadratic complexity.