The Aryabhata Algorithm Using Least Absolute Remainders

TL;DR

This paper introduces the Aryabhata algorithm utilizing least absolute remainders for computing multiplicative inverses and solving linear congruences, potentially offering improved performance in cryptographic applications.

Contribution

It presents a novel exposition of the Aryabhata algorithm that may outperform recent methods by Rao and Yang.

Findings

Potentially faster performance than recent algorithms

Effective in cryptographic applications

Provides a clear exposition of the Aryabhata method

Abstract

This paper presents an introduction to the Aryabhata algorithm for finding multiplicative inverses and solving linear congruences, both of which have applications in cryptography. We do so by the use of the least absolute remainders. The exposition of the Aryabhata algorithm provided here can have performance that could exceed what was described recently by Rao and Yang.