An Algorithm for Solving Two Variable Linear Diophantine Equations

Document Type

Conference Article

Publication Title

Communications in Computer and Information Science

Abstract

In cryptography algorithms like RSA, Elliptic Curve Cryptography, calculation of modulo multiplicative inverse of an integer is required. Calculation of modulo multiplicative inverse problem is a specialized form of solving Diophantine equation. Existing Extended Euclid’s Algorithm solves the Diophantine equation using top down and bottom up method. It firstly, calculates the intermediate values using top down approach then calculates the coefficient values using bottom up approach. The proposed algorithm calculates the intermediate values and coefficient values using only top-down approach. Hence in some cases proposed algorithm takes less computation time to compute the coefficient values of Diophantine equation. The proposed algorithm has been analysed rigorously to obtain a general expression for its efficiency in average case. The results obtained after implementation of the proposed algorithm verify that in some cases proposed algorithm takes lesser time than the existing algorithm.

First Page

35

Last Page

48

DOI

10.1007/978-3-031-37940-6_4

Publication Date

1-1-2023

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