A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS

摘要

The main objective of this work is to build, based on the Euclidean algorithm, a ?matrix of algorithms? Where is a fixed matrix onThe function B is called the algorithmic matrix function. Here we show its properties and some applications to Cryptography and nonlinear Diophantine equations. The case n = m = 1 has particular interest. On this way we show equivalences between B and the Carl Friedrich Gau??s congruence module p.