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 language||American English|
|Number of pages||31|
|State||Published - 1 Dec 2007|
Cortés Vega, L. A., Rojas Castro, D. E., Santiago Ayala, Y. S., & Rojas Romero, S. C. (2007). A technique based on the Euclidean algorithm and its applications to cryptography and nonlinear diophantine equations. Proyecciones, 309-339.