Fractal mathematical over extended finite fields Fp[x]/(f(x))

Abstract: In this paper, we have defined an algorithm for the construction of iterative operations, based on dimensional projections and correspondence between the properties of extended fields, with respect to modular reduction. For a field with product operations R(x) ⊗ D(x), over finite...

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Autor principal:	Sandoval-Ruiz,Cecilia E.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Materias:	Finite Galois extensions Iterative multiplication over GF Fractal design techniques LFSR schemes Self-similar circuits automorphism
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300731
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spelling	oai:scielo:S0716-091720210003007312021-06-07Fractal mathematical over extended finite fields Fp[x]/(f(x))Sandoval-Ruiz,Cecilia E. Finite Galois extensions Iterative multiplication over GF Fractal design techniques LFSR schemes Self-similar circuits automorphism Abstract: In this paper, we have defined an algorithm for the construction of iterative operations, based on dimensional projections and correspondence between the properties of extended fields, with respect to modular reduction. For a field with product operations R(x) ⊗ D(x), over finite fields, GF[(p m ) n−k ]. With G p [x]/(g(f(x)), whence the coefficient of the g(x) is replaced after a modular reduction operation, with characteristic p. Thus, the reduced coefficients of the generating polynomial of G contain embedded the modular reduction and thus simplify operations that contain basic finite fields. The algorithm describes the process of construction of the GF multiplier, it can start at any stage of LFSR; it is shift the sequence of operation, from this point on, thanks to the concurrent adaptation, to optimize the energy consumption of the GF iterative multiplier circuit, we can claim that this method is more efficient. From this, it was realized the mathematical formalization of the characteristics of the iterative operations on the extended finite fields has been developed, we are applying a algorithm several times over the coefficients in the smaller field and then in the extended field, concurrent form.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.3 20212021-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300731en10.22199/issn.0717-6279-4322
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Finite Galois extensions Iterative multiplication over GF Fractal design techniques LFSR schemes Self-similar circuits automorphism
spellingShingle	Finite Galois extensions Iterative multiplication over GF Fractal design techniques LFSR schemes Self-similar circuits automorphism Sandoval-Ruiz,Cecilia E. Fractal mathematical over extended finite fields Fp[x]/(f(x))
description	Abstract: In this paper, we have defined an algorithm for the construction of iterative operations, based on dimensional projections and correspondence between the properties of extended fields, with respect to modular reduction. For a field with product operations R(x) ⊗ D(x), over finite fields, GF[(p m ) n−k ]. With G p [x]/(g(f(x)), whence the coefficient of the g(x) is replaced after a modular reduction operation, with characteristic p. Thus, the reduced coefficients of the generating polynomial of G contain embedded the modular reduction and thus simplify operations that contain basic finite fields. The algorithm describes the process of construction of the GF multiplier, it can start at any stage of LFSR; it is shift the sequence of operation, from this point on, thanks to the concurrent adaptation, to optimize the energy consumption of the GF iterative multiplier circuit, we can claim that this method is more efficient. From this, it was realized the mathematical formalization of the characteristics of the iterative operations on the extended finite fields has been developed, we are applying a algorithm several times over the coefficients in the smaller field and then in the extended field, concurrent form.
author	Sandoval-Ruiz,Cecilia E.
author_facet	Sandoval-Ruiz,Cecilia E.
author_sort	Sandoval-Ruiz,Cecilia E.
title	Fractal mathematical over extended finite fields Fp[x]/(f(x))
title_short	Fractal mathematical over extended finite fields Fp[x]/(f(x))
title_full	Fractal mathematical over extended finite fields Fp[x]/(f(x))
title_fullStr	Fractal mathematical over extended finite fields Fp[x]/(f(x))
title_full_unstemmed	Fractal mathematical over extended finite fields Fp[x]/(f(x))
title_sort	fractal mathematical over extended finite fields fp[x]/(f(x))
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000300731
work_keys_str_mv	AT sandovalruizceciliae fractalmathematicaloverextendedfinitefieldsfpxfx
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Fractal mathematical over extended finite fields Fp[x]/(f(x))

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