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

• Cortés Vega, Luis A. ^[1] ; Rojas Castro, Daniza E. ^[1] ; Santiago Ayala, Yolanda S. ^[2] ; Rojas Romero, Santiago C. ^[2]
  1. [1] Universidad de Antofagasta

     Universidad de Antofagasta

     Antofagasta, Chile

     
  2. [2] Universidad Nacional Mayor de San Marcos

     Universidad Nacional Mayor de San Marcos

     Perú

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 26, Nº. 3, 2007, págs. 309-339
• Idioma: inglés
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• Resumen

  • The main objective of this work is to build, based on the Euclidean algorithm, a “matrix of algorithms” ΦB : N∗ m×n→ N∗ m×n , with ΦB(A)=(Φbij (aij )), where B = (bij )1≤i≤m1≤j≤n is a fixed matrix on N∗ m×n. The function ΦB 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 ΦB and the Carl Friedrich Gauβ’s congruence module p.