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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

CORTES VEGA, LUIS A.; ROJAS CASTRO, DANIZA E.; SANTIAGO AYALA, YOLANDA S.  and  ROJAS ROMERO, SANTIAGO C.. A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS. Proyecciones (Antofagasta) [online]. 2007, vol.26, n.3, pp.309-339. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172007000300007.

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 Gauߒs congruence module p.

Keywords : Algorithmic matrix function; Euclidean algorithm; non-linear Diophantine equations; message codification and decoding; Gauߒs congruence module p.

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