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New classes of nearly optimal time-hopping sequence sets for UWB systems 一类新的超宽带系统近最优跳时序列集
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/amc.2023018
Peihua Li, Xingyu Zheng, Cuiling Fan
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引用次数: 0
A coercion-resistant blockchain-based E-voting protocol with receipts 一种带有收据的基于区块链的抗强制电子投票协议
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021005
Chiara Spadafora, Riccardo Longo, M. Sala
We propose a decentralized e-voting protocol that is coercion-resistant and vote-selling resistant, while being also completely transparent and not receipt-free. We achieve decentralization using blockchain technology. Because of the properties such as transparency, decentralization, and non-repudiation, blockchain is a fundamental technology of great interest in its own right, and it also has large potential when integrated into many other areas. We prove the security of the protocol under the standard DDH assumption on the underlying prime-order cyclic group (e.g. the group of points of an elliptic curve), as well as under standard assumptions on blockchain robustness.
我们提出了一种去中心化的电子投票协议,该协议具有抗胁迫和抗投票销售的能力,同时也是完全透明的,并且不是无收据的。我们使用区块链技术实现去中心化。由于具有透明性、去中心化和不可抵赖性等特性,区块链本身就是一项令人非常感兴趣的基础技术,并且在集成到许多其他领域时也具有巨大的潜力。我们证明了协议在标准DDH假设下的安全性,以及在区块链鲁棒性的标准假设下的安全性。
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引用次数: 4
Lee metrics on groups 李组度量
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-06-09 DOI: 10.3934/amc.2023011
Ricardo A. Podest'a, Maximiliano G. Vides
In this work we consider interval metrics on groups; that is, integral invariant metrics whose associated weight functions do not have gaps. We give conditions for a group to have and to have not interval metrics. Then we study Lee metrics on general groups, that is interval metrics having the finest unitary symmetric associated partition. These metrics generalize the classic Lee metric on cyclic groups. In the case that $G$ is a torsion-free group or a finite group of odd order, we prove that $G$ has a Lee metric if and only if $G$ is cyclic. Also, if $G$ is a group admitting Lee metrics then $G times mathbb{Z}_2^k$ always have Lee metrics for every $k in mathbb{N}$. Then, we show that some families of metacyclic groups, such as cyclic, dihedral, and dicyclic groups, always have Lee metrics. Finally, we give conditions for non-cyclic groups such that they do not have Lee metrics. We end with tables of all groups of order $le 31$ indicating which of them have (or have not) Lee metrics and why (not).
在这项工作中,我们考虑了群上的区间度量;也就是说,其相关权函数没有间隙的积分不变度量。我们给出了群有和没有区间度量的条件。然后研究了一般群上的李度量,即具有最优酉对称关联划分的区间度量。这些度量推广了环群上的经典李度量。在$G$是无扭群或奇阶有限群的情况下,证明$G$有李度规当且仅当$G$是循环的。同样,如果$G$是一个允许Lee度量的群,那么$G 乘以mathbb{Z}_2^k$对于mathbb{N}$中的每一个$k 总是有Lee度量。然后,我们证明了一些亚环群族,如环、二面体和双环群,总是有李度量。最后,我们给出了非循环群没有李测度的条件。最后,我们以顺序为$le 31$的所有组的表结束,指出其中哪些组有(或没有)Lee度量以及为什么(没有)Lee度量。
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引用次数: 0
Weierstrass semigroups on the third function field in a tower attaining the Drinfeld-Vlăduţ bound 塔上第三函数域上的Weierstrass半群达到了drinfeld - vl<e:1>界
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-01-01 DOI: 10.3934/amc.2022066
Shudi Yang, Chuangqiang Hu

For applications in algebraic geometry codes, an explicit description of bases of the Riemann-Roch spaces over function fields is needed. We investigate the third function field begin{document}$ F^{(3)} $end{document} in a tower of Artin-Schreier extensions described by Garcia and Stichtenoth reaching the Drinfeld-Vlăduţ bound. We construct new bases for the related Riemann-Roch spaces of begin{document}$ F^{(3)} $end{document} and present some basic properties of divisors on a line. From the bases, we explicitly calculate the Weierstrass semigroups and pure gaps at several places on begin{document}$ F^{(3)} $end{document}. All of these results can be viewed as a generalization of the previous work done by Voss and Høholdt (1997).

For applications in algebraic geometry codes, an explicit description of bases of the Riemann-Roch spaces over function fields is needed. We investigate the third function field begin{document}$ F^{(3)} $end{document} in a tower of Artin-Schreier extensions described by Garcia and Stichtenoth reaching the Drinfeld-Vlăduţ bound. We construct new bases for the related Riemann-Roch spaces of begin{document}$ F^{(3)} $end{document} and present some basic properties of divisors on a line. From the bases, we explicitly calculate the Weierstrass semigroups and pure gaps at several places on begin{document}$ F^{(3)} $end{document}. All of these results can be viewed as a generalization of the previous work done by Voss and Høholdt (1997).
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引用次数: 1
Introduction to the special issue dedicated to Cunsheng Ding on the occasion of his 60th birthday 丁存生60大寿特刊简介
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-01-01 DOI: 10.3934/amc.2022089
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引用次数: 0
Reconstructing points of superelliptic curves over a prime finite field 素数有限域上超椭圆曲线点的重构
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-01-01 DOI: 10.3934/amc.2022022
J. Gutierrez

Let begin{document}$ p $end{document} be a prime and begin{document}$ mathbb{F}_p $end{document} the finite field with begin{document}$ p $end{document} elements. We show how, when given an superelliptic curve begin{document}$ Y^n+f(X) in mathbb{F}_p[X,Y] $end{document} and an approximation to begin{document}$ (v_0,v_1) in mathbb{F}_p^2 $end{document} such that begin{document}$ v_1^n = -f(v_0) $end{document}, one can recover begin{document}$ (v_0,v_1) $end{document} efficiently, if the approximation is good enough. As consequence we provide an upper bound on the number of roots of such bivariate polynomials where the roots have certain restrictions. The results has been motivated by the predictability problem for non-linear pseudorandom number generators and, other potential applications to cryptography.

Let begin{document}$ p $end{document} be a prime and begin{document}$ mathbb{F}_p $end{document} the finite field with begin{document}$ p $end{document} elements. We show how, when given an superelliptic curve begin{document}$ Y^n+f(X) in mathbb{F}_p[X,Y] $end{document} and an approximation to begin{document}$ (v_0,v_1) in mathbb{F}_p^2 $end{document} such that begin{document}$ v_1^n = -f(v_0) $end{document}, one can recover begin{document}$ (v_0,v_1) $end{document} efficiently, if the approximation is good enough. As consequence we provide an upper bound on the number of roots of such bivariate polynomials where the roots have certain restrictions. The results has been motivated by the predictability problem for non-linear pseudorandom number generators and, other potential applications to cryptography.
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引用次数: 2
$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $-additive cyclic codes $ mathbb {Z} _ {p r ^} mathbb {Z} _ {p s ^} mathbb {Z} _ {p ^ t} $添加剂循环码
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-01-01 DOI: 10.3934/amc.2022079
Raziyeh Molaei, K. Khashyarmanesh

Let begin{document}$ p $end{document} be a prime number and begin{document}$ r, s, t $end{document} be positive integers such that begin{document}$ rle sle t $end{document}. A begin{document}$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $end{document}-additive code is a begin{document}$ mathbb{Z}_{p^t} $end{document}-submodule of begin{document}$ mathbb{Z}_{p^r}^{alpha} times mathbb{Z}_{p^s}^{beta} times mathbb{Z}_{p^t}^{gamma} $end{document}, where begin{document}$ alpha, beta, gamma $end{document} are positive integers. In this paper, we study begin{document}$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $end{document}-additive cyclic codes. In fact, we show that these codes can be identified as submodules of the ring begin{document}$ R = mathbb{Z}_{p^r}[x]/big times mathbb{Z}_{p^s}[x]/big times mathbb{Z}_{p^t}[x]/big $end{document}. Furthermore, we determine the generator polynomials and minimum generating sets of this kind of codes. Moreover, we investigate their dual codes.

Let begin{document}$ p $end{document} be a prime number and begin{document}$ r, s, t $end{document} be positive integers such that begin{document}$ rle sle t $end{document}. A begin{document}$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $end{document}-additive code is a begin{document}$ mathbb{Z}_{p^t} $end{document}-submodule of begin{document}$ mathbb{Z}_{p^r}^{alpha} times mathbb{Z}_{p^s}^{beta} times mathbb{Z}_{p^t}^{gamma} $end{document}, where begin{document}$ alpha, beta, gamma $end{document} are positive integers. In this paper, we study begin{document}$ mathbb{Z}_{p^r}mathbb{Z}_{p^s}mathbb{Z}_{p^t} $end{document}-additive cyclic codes. In fact, we show that these codes can be identified as submodules of the ring begin{document}$ R = mathbb{Z}_{p^r}[x]/big times mathbb{Z}_{p^s}[x]/big times mathbb{Z}_{p^t}[x]/big $end{document}. Furthermore, we determine the generator polynomials and minimum generating sets of this kind of codes. Moreover, we investigate their dual codes.
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引用次数: 1
Optimal wide-gap-zone frequency hopping sequences 最优宽间隙区跳频序列
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-01-01 DOI: 10.3934/amc.2022097
Qin Shu, Hai Liu, Xing Liu, Yun-xiu Yang, Wendong Chen
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引用次数: 0
Improved lower bounds for self-dual codes over $ mathbb{F}_{11} $, $ mathbb{F}_{13} $, $ mathbb{F}_{17} $, $ mathbb{F}_{19} $ and $ mathbb{F}_{23} $ 改进了$ mathbb{F}_{11} $、$ mathbb{F}_{13} $、$ mathbb{F}_{17} $、$ mathbb{F}_{19} $和$ mathbb{F}_{23} $上的自对偶码的下界
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-01-01 DOI: 10.3934/amc.2022083
T. Gulliver, M. Harada

We construct self-dual codes over begin{document}$ mathbb{F}_{11} $end{document}, begin{document}$ mathbb{F}_{13} $end{document}, begin{document}$ mathbb{F}_{17} $end{document}, begin{document}$ mathbb{F}_{19} $end{document} and begin{document}$ mathbb{F}_{23} $end{document} which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual begin{document}$ [n, n/2] $end{document} codes over begin{document}$ mathbb{F}_{p} $end{document} is determined for begin{document}$ (p, n) = (19, 24) $end{document} and begin{document}$ (23, 28) $end{document}.

We construct self-dual codes over begin{document}$ mathbb{F}_{11} $end{document}, begin{document}$ mathbb{F}_{13} $end{document}, begin{document}$ mathbb{F}_{17} $end{document}, begin{document}$ mathbb{F}_{19} $end{document} and begin{document}$ mathbb{F}_{23} $end{document} which improve the previously known lower bounds on the largest minimum weights. In particular, the largest possible minimum weight among self-dual begin{document}$ [n, n/2] $end{document} codes over begin{document}$ mathbb{F}_{p} $end{document} is determined for begin{document}$ (p, n) = (19, 24) $end{document} and begin{document}$ (23, 28) $end{document}.
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引用次数: 0
Finding small roots for bivariate polynomials over the ring of integers 寻找整数环上二元多项式的小根
IF 0.9 4区 计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2022-01-01 DOI: 10.3934/amc.2022012
Jiseung Kim, Changmin Lee

In this paper, we propose the first heuristic algorithm for finding small roots for a bivariate equation modulo an ideal begin{document}$ mathcal{I} $end{document} over the ring of integers begin{document}$ mathcal{R} $end{document}. Existing algorithms for solving polynomial equations with size constraints only work for bivariate modular equations over integers, and univariate modular equation over number fields.

Both previous algorithms use a relation between the short vector in a skillfully structured lattice and a size constrained solution. Our algorithm also follows this framework, but we additionally use a polynomial factoring algorithm over number fields to recover a 'ring' root of a bivariate polynomial equation.

As a result, when an LLL algorithm is employed to find a short vector, we can recover all small roots of a bivariate polynomial modulo begin{document}$ mathcal{I} $end{document} in polynomial time under some constraint.

In this paper, we propose the first heuristic algorithm for finding small roots for a bivariate equation modulo an ideal begin{document}$ mathcal{I} $end{document} over the ring of integers begin{document}$ mathcal{R} $end{document}. Existing algorithms for solving polynomial equations with size constraints only work for bivariate modular equations over integers, and univariate modular equation over number fields.Both previous algorithms use a relation between the short vector in a skillfully structured lattice and a size constrained solution. Our algorithm also follows this framework, but we additionally use a polynomial factoring algorithm over number fields to recover a 'ring' root of a bivariate polynomial equation.As a result, when an LLL algorithm is employed to find a short vector, we can recover all small roots of a bivariate polynomial modulo begin{document}$ mathcal{I} $end{document} in polynomial time under some constraint.
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引用次数: 0
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Advances in Mathematics of Communications
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