TY - JOUR

T1 - A technique based on the Euclidean algorithm and its applications to cryptography and nonlinear diophantine equations

AU - Cortés Vega, Luis A.

AU - Rojas Castro, Daniza E.

AU - Santiago Ayala, Yolanda S.

AU - Rojas Romero, Santiago C.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - 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.

AB - 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.

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M3 - Article

SP - 309

EP - 339

JO - Proyecciones

JF - Proyecciones

SN - 0716-0917

ER -