This paper presents the innovative notion of a "neutrosophic supra bi-topological space," which serves as an expansion of both neutrosophic supra topological space and bitopological space. ...Furthermore, we delve into various categories of open and closed sets within this framework, including concepts like pairwise neutrosophic supra open sets, pairwise neutrosophic supra semi-open sets, and pairwise neutrosophic supra pre-open sets. Additionally, we formulate a few outcomes in the form of theorems, propositions, and lemmas.
Permutation is a natural phenomenon useful for understanding and explaining the structural and functional behavior of objects or concepts. The mathematical formulation of permutation behavior can be ...readily achieved by permutation polynomials. Permutation polynomials are constructed by suitably modifying linearized polynomials and associated affine polynomials with the help of additive characters, multiplicative characters, and special types of Trace functions for the polynomials in one and more than one indeterminates. The permutation properties of the obtained polynomials are verified using the AGW criterion.
Constructing permutation polynomials is a hot topic in the area of finite fields, and permutation polynomials have many applications in different areas. Recently, several classes of permutation ...trinomials were constructed. In 2015, Hou surveyed the achievements of permutation polynomials and novel methods. But, very few were known at that time. Recently, many permutation binomials and trinomials have been constructed. Here we survey the significant contribution made to the construction of permutation trinomials over finite fields in recent years. Emphasis is placed on significant results and novel methods. The covered material is split into three aspects: the existence of permutation trinomials of the respective forms $ x^{r}h(x^{s}) $, $ \lambda_{1}x^{a}+\lambda_{2}x^{b}+\lambda_{3}x^{c} $ and $ x+x^{s(q^{m}-1)+1} +x^{t(q^{m}-1)+1} $, with Niho-type exponents $ s, t $.
Introduction to NeutroNearrings Vadiraja, Bhatta G. R; Manasa, K. J; Gautham, Shenoy B ...
Neutrosophic sets and systems,
12/2021, Letnik:
46
Journal Article
Recenzirano
Odprti dostop
Algebraic concepts and structures are enriched with the special types of operations and axioms known as NeutroOperations and NeutroAxioms. Various types of NeutroAlgebras are studied using several ...such defined concepts. The objective of this paper is to introduce the concept of NeutroNearrings. Several interesting results and examples of NeutroNearrings, NeutroSubRings, NeutroQuotientNearrings and NeutroNearringHo-momorphisms are presented. Keywords: Nearring; NeutroRings; NeutroNearring; Neutrosophy.
Boolean functions play an important role in symmetric cryptosystems. In this paper, we have constructed near-bent Boolean functions algebraically with the help of Niho power function exponent in the ...trace form over a finite field. Specific cryptographic properties which may gain attention with suitable modifications are observed using these functions. If exponents are either Mersenne numbers or Fermat numbers, then the resulting functions are found to be APN (almost perfect nonlinear).
In this paper, we extend the concepts of Neutrosophy to Boolean function and define ClassicalBalanced, AntiBalanced and NeutroBalanced functions. We consider functions of the form f(x) = Tr(x.sup.d), ...where the exponent d may be Gold exponent, Kasami exponent, Welch exponent or any arbitrary positive integer. We, for different values of d, examine nature of these functions with respect to the above stated three categories. Keywords: Balanced function; Neutrosophy; AntiBalanced function; NeutroBalanced function; Cryptography.
Abstract A polynomial can represent every function from a finite field to itself. The functions which are also permutations of the field give rise to permutation polynomials, which have potential ...applications in cryptology and coding theory. Permutation polynomials over finite rings are studied with respect to the sequences they generate. The sequences obtained through some permutation polynomials are tested for randomness by carrying out known statistical tests. Random number generation plays a major role in cryptography and hence permutation polynomials may be used as random number generators.
Orthogonal properties of Latin squares represented by permutation polynomials are discussed. Pairs of bivariate polynomials over small rings are considered.
Our work is motivated by a recent paper of Rivest 6, concerning permutation polynomials over the rings Zn with n = 2w. Permutation polynomials over finite fields and the rings Zn have lots of ...applications, including cryptography. For the special case n = 2w, a characterization has been obtained in 6 where it is shown that such polynomials can form a Latin square (0 ≤ x,y ≤ n - 1) if and only if the four univariate polynomials P(x, 0),P(x, 1),P(0,y) and P(1,y) are permutation polynomials. Further, it is shown that pairs of such polynomials will never form Latin squares. In this paper, we consider bivariate polynomials P(x,y) over the rings Zn when n ≠ 2w. Based on preliminary numerical computations, we give complete results for linear and quadratic polynomials. Rivest's result holds in the linear case while there are plenty of counterexamples in the quadratic case.
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