Results 41 to 50 of about 12,890,521 (357)
Strict avalanche criterion over finite fields
Journal of Mathematical Cryptology, 2007 Boolean functions which satisfy the Strict Avalanche Criterion (SAC) play an important role in the art of information security. In this paper, we extend the concept of SAC to finite fields GF(p).
Li Yuan, Cusick T. W.
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A Generalization of APN Functions for Odd Characteristic [PDF]
, 2016 Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on.
Kuroda, Masamichi, Tsujie, Shuhei
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The existence of $\protect \mathbb{F}_q$-primitive points on curves using freeness
Comptes Rendus. Mathématique, 2022 Let $\mathcal{C}_Q$ be the cyclic group of order $Q$, $n$ a divisor of $Q$ and $r$ a divisor of $Q/n$. We introduce the set of $(r,n)$-free elements of $\mathcal{C}_Q$ and derive a lower bound for the number of elements $\theta \in \mathbb{F}_q$ for ...
Cohen, Stephen D. +2 more
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Self-dual codes and orthogonal matrices over large finite fields
Finite Fields Their Appl., 2018 In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, code extension and projection over a self-dual basis are the main tools.
Minjia Shi +3 more
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On Fields with Finite Information Density [PDF]
, 2004 The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory ...
A. Kempf +25 more
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Discrete logarithm problem in matrix
Lietuvos Matematikos Rinkinys, 2023 In this paper the discrete logarithm problem in matrix in finite fields is formulated, possible ways of solution are given.
Povilas Tvarijonas +2 more
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Distribution of constant terms of irreducible polynomials in ℤₚ[x] whose degree is a product of two distinct odd primes [PDF]
Notes on Number Theory and Discrete MathematicsWe obtain explicit formulas for the number of monic irreducible polynomials with prescribed constant term and degree q₁q₂ over a finite field, where q₁ and q₂ are distinct odd primes. These formulas are derived from work done by Yucas.
Sarah C. Cobb +4 more
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Two Families of Optimal Ternary Cyclic Codes With Two Zeros
IEEE Access, 2022 Cyclic codes are an important subclass of linear codes and have wide applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms.
Jinmei Fan, Binseng Wang
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A Small Subgroup Attack on Bitcoin Address Generation
Mathematics, 2020 We show how a small subgroup confinement-like attack may be mounted on the Bitcoin addresses generation protocol, by inspecting a special subgroup of the group associated to point multiplication.
Massimiliano Sala +2 more
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Calculation of Fourier-Galois transforms in reduced binary number systems [PDF]
Компьютерная оптика, 2018 The paper proposes a new method for calculating Fourier-Galois transforms (number-theoretical transforms), which are a modular analog of the discrete Fourier transform.
Vladimir Chernov
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