Results 61 to 70 of about 98,739 (338)
On Inverses of Permutation Polynomials of Small Degree Over Finite Fields [PDF]
IEEE Transactions on Information Theory, 2018 Permutation polynomials (PPs) and their inverses have applications in cryptography, coding theory and combinatorial design theory. In this paper, we make a brief summary of the inverses of PPs of finite fields, and give the inverses of all PPs of degree ≤
Yanbin Zheng, Qiang Wang, Wenhong Wei
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Multiplication polynomials and relative Manin-Mumford [PDF]
, 2015 After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is $(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
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Factoring polynomials over arbitrary finite fields [PDF]
, 2000 We analyse an extension of Shoup's (Inform. Process. Lett. 33 (1990) 261–267) deterministic algorithm for factoring polynomials over finite prime fields to arbitrary finite fields.
Lange, Tanja +5 more
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On the Structure of Valiant's Complexity Classes [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 In Valiant developed an algebraic analogue of the theory of NP-completeness for computations of polynomials over a field. We further develop this theory in the spirit of structural complexity and obtain analogues of well-known results by Baker, Gill, and
Peter Bürgisser
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Deterministic Construction of Compressed Sensing Matrices via Vector Spaces Over Finite Fields
IEEE Access, 2020 Compressed Sensing (CS) is a new signal processing theory under the condition that the signal is sparse or compressible. One of the central problems in compressed sensing is the construction of sensing matrices.
Xuemei Liu, Lihua Jia
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Classes of weak Dembowski–Ostrom polynomials for multivariate quadratic cryptosystems
Journal of Mathematical Cryptology, 2015 T. Harayama and D. K. Friesen [J. Math. Cryptol. 1 (2007), 79–104] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski–Ostrom (DO) polynomials in this framework over the finite field 𝔽2.
Alam Bilal, Özbudak Ferruh, Yayla Oğuz
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Polynomials over Finite Fields [PDF]
, 2020 U ovom radu bavili smo se polinomima i njihovim svojstvima, a posebno svojstvima polinoma nad konačnim poljima. U prvom poglavlju dane su osnovne definicije i tvrdnje vezane uz djeljivost polinoma, faktorizaciju, korijene i ireducibilnost polinoma jedne
Bročić, Lucija
core
On the Heuristic of Approximating Polynomials over Finite Fields by Random Mappings [PDF]
arXiv.org, 2015 The study of iterations of functions over a finite field and the corresponding functional graphs is a growing area of research with connections to cryptography.
Rodrigo S. V. Martins, D. Panario
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Characterization and Enumeration of Good Punctured Polynomials over Finite Fields
International Journal of Mathematics and Mathematical Sciences, 2016 A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary field F2.
Somphong Jitman +4 more
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Nilpotent linearized polynomials over finite fields and applications [PDF]
Finite Fields Their Appl., 2016 Let $q$ be a prime power and $\mathbb F_{q^n}$ be the finite field with $q^n$ elements, where $n>1$. We introduce the class of the linearized polynomials $L(x)$ over $\mathbb F_{q^n}$ such that $$L^{(t)}(x):=\underbrace{L(L(\cdots(x)\cdots))}_{t \quad ...
Lucas Reis
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