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

The main objective of this work is to build, based on the Euclidean algorithm, a matrix of algorithms <img border=0 width=476 height=41 id="_x0000_i1032" src="../img/formula1.JPG"> Where <img border=0 width=196 height=28 id="_x0000_i1031" src="../img/for...

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Autores principales:	CORTÉS VEGA,LUIS A., ROJAS CASTRO,DANIZA E., SANTIAGO AYALA,YOLANDA S., ROJAS ROMERO,SANTIAGO C.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2007
Materias:	Algorithmic matrix function Euclidean algorithm non-linear Diophantine equations message codification and decoding Gaußs congruence module p
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000300007
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spelling	oai:scielo:S0716-091720070003000072008-01-28A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONSCORTÉS VEGA,LUIS A.ROJAS CASTRO,DANIZA E.SANTIAGO AYALA,YOLANDA S.ROJAS ROMERO,SANTIAGO C. Algorithmic matrix function Euclidean algorithm non-linear Diophantine equations message codification and decoding Gaußs congruence module p The main objective of this work is to build, based on the Euclidean algorithm, a matrix of algorithms <img border=0 width=476 height=41 id="_x0000_i1032" src="../img/formula1.JPG"> Where <img border=0 width=196 height=28 id="_x0000_i1031" src="../img/formula2.JPG">is a fixed matrix on<img border=0 width=68 height=29 id="_x0000_i1030" src="../img/formula3.JPG">The function <img border=0 width=17 height=20 id="_x0000_i1029" src="../img/formula4.JPG">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 <img border=0 width=17 height=20 id="_x0000_i1028" src="../img/formula4.JPG">B and the Carl Friedrich Gaußs congruence module p.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.26 n.3 20072007-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000300007en10.4067/S0716-09172007000300007
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Algorithmic matrix function Euclidean algorithm non-linear Diophantine equations message codification and decoding Gaußs congruence module p
spellingShingle	Algorithmic matrix function Euclidean algorithm non-linear Diophantine equations message codification and decoding Gaußs congruence module p CORTÉS VEGA,LUIS A. ROJAS CASTRO,DANIZA E. SANTIAGO AYALA,YOLANDA S. ROJAS ROMERO,SANTIAGO C. A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS
description	The main objective of this work is to build, based on the Euclidean algorithm, a matrix of algorithms <img border=0 width=476 height=41 id="_x0000_i1032" src="../img/formula1.JPG"> Where <img border=0 width=196 height=28 id="_x0000_i1031" src="../img/formula2.JPG">is a fixed matrix on<img border=0 width=68 height=29 id="_x0000_i1030" src="../img/formula3.JPG">The function <img border=0 width=17 height=20 id="_x0000_i1029" src="../img/formula4.JPG">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 <img border=0 width=17 height=20 id="_x0000_i1028" src="../img/formula4.JPG">B and the Carl Friedrich Gaußs congruence module p.
author	CORTÉS VEGA,LUIS A. ROJAS CASTRO,DANIZA E. SANTIAGO AYALA,YOLANDA S. ROJAS ROMERO,SANTIAGO C.
author_facet	CORTÉS VEGA,LUIS A. ROJAS CASTRO,DANIZA E. SANTIAGO AYALA,YOLANDA S. ROJAS ROMERO,SANTIAGO C.
author_sort	CORTÉS VEGA,LUIS A.
title	A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS
title_short	A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS
title_full	A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS
title_fullStr	A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS
title_full_unstemmed	A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS
title_sort	technique based on the euclidean algorithm and its applications to cryptography and nonlinear diophantine equations
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2007
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000300007
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A TECHNIQUE BASED ON THE EUCLIDEAN ALGORITHM AND ITS APPLICATIONS TO CRYPTOGRAPHY AND NONLINEAR DIOPHANTINE EQUATIONS

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