A matrix numerical methods comparative study in modular inverse computation with a symmetric cryptography perspective

Abstract

This document describes the analysis carried out in terms of execution time, processing and use of random access memory, to characterize the efficiency of two matrix numerical methods, which are Gauss-Jacques with implicit Euclidean modularization and Gauss-Jordan with explicit modularization. Both methods compute the modular inverse of any given matrix in Zn. The initial matrix is known as the Key in the context of symmetric cryptography. The tests carried out considered multiple matrix-size in order to allow us identify the behavior of each method, and the resources that each one uses in terms of processing and memory to determine which is the most efficient method in the computational context.