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




Finite Galois extensions, Iterative multiplication over GF, Fractal design techniques, LFSR schemes, Self-similar circuits automorphism


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[(pm)n−k]. With Gp[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  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 Biography

Cecilia E. Sandoval-Ruiz, Universidad de Carabobo.

Instituto de matemática y cálculo aplicado, Facultad de Ingeniería.


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How to Cite

C. E. Sandoval-Ruiz, “Fractal mathematical over extended finite fields Fp[x]/(f(x))”, Proyecciones (Antofagasta, On line), vol. 40, no. 3, pp. 731-742, May 2021.