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
SN - 0716-0917
SP - 309
EP - 339
JO - Proyecciones
JF - Proyecciones
ER -