A general method for to decompose modular multiplicative inverse operators over Group of units

Vega, Luis A. Cortés

doi:10.4067/s0716-09172018000200265

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…This has advantages in the circuit of operations over finite fields, in the areas of mathematics and engineering. (iii) Technique for the generation of structures for the parallel implementation of modular arithmetic [6], over finite field, where the number of component operations and their ordering is simplified and minimized.…”

Section: Discussionmentioning

confidence: 99%

“…From the study of the extended finite fields and its properties, the description of the fractal (concatenated) operation of multiplication for extended fields was developed in this investigation, from a circuit interpretation LFSR [5] (see Figure 1). The modular arithmetic can be applied in Cryptography, Theory of Code, Circuits on Systems, Galois Theory and Digital Communications and other areas as extended GF (see, for instance, [6][7] and references therein). This analysis starts from the study of the mathematical model of the polynomial representation, in which: If p(x) is the irreducible polynomial, then the multiplication of two elements of the field, represented as the polynomials A(x) and B(x) is the algebraic product of the two polynomials, and the module operation of the polynomial p(x), also known as modular reduction:…”

Section: Introductionmentioning

confidence: 99%

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

Ruiz

2021

Proyecciones (Antofagasta)

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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 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.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ruiz

2021

Proyecciones (Antofagasta)

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A refined version of the inverse decomposition theorem for modular multiplicative inverse operators

Cortés-Vega

2021

J. Phys.: Conf. Ser.

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Recently, we started in the IOP Conference Series [1, 2] and in [3] the study of modular multiplicative inverse operators in an algorithmic functional context on (ℤ/ϱℤ)* with ϱ > 3, where it is possible to distinguish different formulas that break up these operators over (ℤ/ϱℤ)*, all this thanks to the so-called “inverse decomposition theorem (IDT)”. In this paper, we will study these issues a little deeper. Though we mainly focus the paper on derived for these operators a refined version of the (IDT), also appear on the scene some additional contributions. Finally, in a brief overview, we compare the differences that exist among the new result here established and the old ones. However, along with this, there are still plenty of questions to be answered in this research field.

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A new decomposition law for inverses modular multiplicative on (ℤ/ϱℤ)

Cortés-Vega

2021

J. Phys.: Conf. Ser.

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In modular arithmetic, we find a valuable concept, the so-called “modular multiplicative inverse” (symbolized by MMI). In precise words, if ℤ/ϱℤ denoted the residue system modulo ϱ, the (MMI) of a ∈ ℤ/ϱℤ, if it exists, is a −1 ∈ ℤ/ϱℤ, such that a × a − 1 ≡ 1 mod ϱ , where p ≡ q mod ϱ is the usual modular representation of q ∈ ℤ/ϱℤ. This very special element it is one of the most wideley used mathematical concept in science, engineering and subject areas include the particle physics, the analysis and design of algorithms, data structures, databases, and computer architecture. In this paper, we establish a promising decomposition law for (MMI). In this respect, the main purpose of this paper it is shown that it is possible to express the (MMI) in terms of certain modular multiplicative inverse operators (MMIO) all, well-defined on Group of units pre-established. The main point to note here is that the result of this paper, which expands a result originally presented in [3], does not include any special conditions on the parameters involved.

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A general method for to decompose modular multiplicative inverse operators over Group of units

Cited by 3 publications

References 32 publications

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

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

A refined version of the inverse decomposition theorem for modular multiplicative inverse operators

A new decomposition law for inverses modular multiplicative on (ℤ/ϱℤ)

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