Results 71 to 80 of about 127,631 (176)

Polynomial bound for the partition rank vs the analytic rank of tensors

Discrete Analysis, 2020
Polynomial bound for the partition rank vs the analytic rank of tensors, Discrete Analysis 2020:7, 18 pp. There are a number of proofs in additive combinatorics that involve bilinear forms on $\mathbb F_p^n$ that split into a high-rank case and a low ...
Oliver Janzer
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A circuit area optimization of MK-3 S-box

Cybersecurity
In MILCOM 2015, Kelly et al. proposed the authentication encryption algorithm MK-3, which applied the 16-bit S-box. This paper aims to implement the 16-bit S-box with less circuit area. First, we classified the irreducible polynomials over $$\mathbb {F}_{
Yanjun Li, Weiguo Zhang, Yiping Lin, Jian Zou, Jian Liu   +4 more
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Feasibility of primality in bounded arithmetic

Forum of Mathematics, Sigma
We prove the correctness of the AKS algorithm [1] within the bounded arithmetic theory $T^{\text {count}}_2$ or, equivalently, the first-order consequences of the theory $\text {VTC}^0$ expanded by the smash function, which we denote by
Raheleh Jalali, Ondřej Ježil
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Relative rank and regularization

Forum of Mathematics, Sigma
We introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength).
Amichai Lampert, Tamar Ziegler
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Weil sum for birthday attack in multivariate quadratic cryptosystem

Journal of Mathematical Cryptology, 2007
We propose a new cryptanalytic application of a number theoretic tool Weil sum to birthday attack against multivariate quadratic trapdoor function.
Harayama Tomohiro, Friesen Donald K.
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Towards Classification of Fracton Phases: The Multipole Algebra

Physical Review X, 2019
We present an effective field theory approach to the fracton phases. The approach is based on the notion of a multipole algebra. It is an extension of space(time) symmetries of a charge-conserving matter that includes global symmetries responsible for ...
Andrey Gromov
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Normal points on Artin–Schreier curves over finite fields

Comptes Rendus. Mathématique
In 2022, S. D. Cohen and the two authors introduced and studied the concept of $(r, n)$-freeness on finite cyclic groups $G$ for suitable integers $r$, $n$, which is an arithmetic way of capturing elements of special forms that lie in the subgroups of $G$
Kapetanakis, Giorgos, Reis, Lucas
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Dickson polynomials over finite fields

Finite Fields and Their Applications, 2012
For any element \(a\) of a finite field \({\mathbb F}_q\) and any integers \(n\geq 1\), \(k\geq 0\), the authors define the \(n\)-th Dickson polynomial of the \((k+1)\)-st kind \(D_{n,k}(x,a)\) over \({\mathbb F}_q\) by \[ D_{n,k}(x,a) =\sum _{i=0}^{n/2} \frac{n-ki}{n-i} \binom{n-i}{i} (-a)^ix^{n-2i}. \] Moreover, for \(n=0\) one puts \(D_{n,k}(x,a) =2-
Wang, Qiang, Yucas, Joseph L.
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Lookup Table-Based Design of Scalar Multiplication for Elliptic Curve Cryptography

Cryptography
This paper is aimed at using a lookup table method to improve the scalar multiplication performance of elliptic curve cryptography. The lookup table must be divided into two polynomials and requires two iterations of point doubling operation, for which ...
Yan-Duan Ning, Yan-Haw Chen, Cheng-Sin Shih, Shao-I Chu   +3 more
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Polynomial automorphisms over finite fields

, 2001
Every automorphism of the polynomial algebra in \(n\) variables over a field \(k\) induces a bijection of the set \(k^n\) of \(n\)-tuples and in this way the automorphism group maps in the group of all bijections of \(k^n\). It is easy to see that for infinite fields very few bijections are images of automorphisms.
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