A technique based on the Euclidean algorithm and its applications to cryptography and nonlinear diophantine equations

Luis A. Cortés Vega, Daniza E. Rojas Castro, Yolanda S. Santiago Ayala, Santiago C. Rojas Romero

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The main objective of this work is to build, based on the Euclidean algorithm, a "matrix of algorithms" φB:N mxn*→N*mxn, with φ B(A) = (φbij(αij)), where B = (bij)1≤i≤m1≤j≤n is a fixed matrix on N*mxn. The function 2fB is called the algorithmic matrix function. Hem 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 φB and the Carl Friedrich Gauβ's congruence module p.
Original languageAmerican English
Pages (from-to)309-339
Number of pages31
JournalProyecciones
StatePublished - 1 Dec 2007

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