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: | , , , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2007
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000300007 |
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| Sumario: | 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. |
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