Resumen de 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

• 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.