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Exp function for Edwards curves over local fields 局部场上Edwards曲线的Exp函数
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-03-17 DOI: 10.3934/amc.2023012
G. Filippone
{"title":"Exp function for Edwards curves over local fields","authors":"G. Filippone","doi":"10.3934/amc.2023012","DOIUrl":"https://doi.org/10.3934/amc.2023012","url":null,"abstract":"We extend the map Exp for elliptic curves in short Weierstrass form over $ mathbb{C} $ to Edwards curves over local fields. Subsequently, we compute the map Exp for Edwards curves over the local field $ mathbb{Q}_{p} $ of $ p $-adic numbers.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74302701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
$textsf{LightMAC}$: Fork it and make it faster $textsf{LightMAC}$:分叉它，使它更快
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2022100
N. Datta, Avijit Dutta, Cuauhtemoc Mancillas-López
{"title":"$textsf{LightMAC}$: Fork it and make it faster","authors":"N. Datta, Avijit Dutta, Cuauhtemoc Mancillas-López","doi":"10.3934/amc.2022100","DOIUrl":"https://doi.org/10.3934/amc.2022100","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72457442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized bent functions with large dimension 广义大维弯曲函数
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023004
W. Meidl
{"title":"Generalized bent functions with large dimension","authors":"W. Meidl","doi":"10.3934/amc.2023004","DOIUrl":"https://doi.org/10.3934/amc.2023004","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74813536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On covering problems in hierarchical poset spaces 关于层次偏序集空间中的覆盖问题
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2023001
Marco Spreafico, Otávio J. N. T. N. dos Santos, R. A. Machado
{"title":"On covering problems in hierarchical poset spaces","authors":"Marco Spreafico, Otávio J. N. T. N. dos Santos, R. A. Machado","doi":"10.3934/amc.2023001","DOIUrl":"https://doi.org/10.3934/amc.2023001","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81502383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Aperiodic/periodic complementary sequence pairs over quaternions 四元数上的非周期/周期互补序列对
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021063
Zhen Li, Cuiling Fan, Wei Su, Yanfeng Qi
{"title":"Aperiodic/periodic complementary sequence pairs over quaternions","authors":"Zhen Li, Cuiling Fan, Wei Su, Yanfeng Qi","doi":"10.3934/amc.2021063","DOIUrl":"https://doi.org/10.3934/amc.2021063","url":null,"abstract":"<p style='text-indent:20px;'>Aperodic (or called Golay)/Periodic complementary pairs (GCPs/ PCPs) are pairs of sequences whose aperiodic/periodic autocorrelation sums are zero everywhere, except at the zero shift. In this paper, we introduce GCPs/PCPs over the quaternion group <inline-formula><tex-math id=\"M1\">begin{document}$ Q_8 $end{document}</tex-math></inline-formula>, which is a generalization of quaternary GCPs/PCPs. Some basic properties of autocorrelations of <inline-formula><tex-math id=\"M2\">begin{document}$ Q_8 $end{document}</tex-math></inline-formula>-sequences are also obtained. We present three types of constructions for GCPs and PCPs over <inline-formula><tex-math id=\"M3\">begin{document}$ Q_8 $end{document}</tex-math></inline-formula>. The main ideas of these constructions are to consider pairs of a <inline-formula><tex-math id=\"M4\">begin{document}$ Q_8 $end{document}</tex-math></inline-formula>-sequence and its reverse, pairs of interleaving of sequence, or pairs of Kronecker product of sequences. By choosing suitable sequences in these constructions, we obtain new parameters for GCPs and PCPs, which have not been reported before.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85153037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two classes of new optimal ternary cyclic codes 两类新的最优三元循环码
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021033
Yan Liu, X. Cao, W. Lu
{"title":"Two classes of new optimal ternary cyclic codes","authors":"Yan Liu, X. Cao, W. Lu","doi":"10.3934/amc.2021033","DOIUrl":"https://doi.org/10.3934/amc.2021033","url":null,"abstract":"<p style='text-indent:20px;'>Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting subject of study in recent years. The construction of optimal cyclic codes over finite fields is important as they have maximal minimum distance once the length and dimension are given. In this paper, we present two classes of new optimal ternary cyclic codes <inline-formula><tex-math id=\"M1\">begin{document}$ mathcal{C}_{(2,v)} $end{document}</tex-math></inline-formula> by using monomials <inline-formula><tex-math id=\"M2\">begin{document}$ x^2 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M3\">begin{document}$ x^v $end{document}</tex-math></inline-formula> for some suitable <inline-formula><tex-math id=\"M4\">begin{document}$ v $end{document}</tex-math></inline-formula> and explain the novelty of the codes. Furthermore, the weight distribution of <inline-formula><tex-math id=\"M5\">begin{document}$ mathcal{C}_{(2,v)}^{perp} $end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=\"M6\">begin{document}$ v = frac{3^{m}-1}{2}+2(3^{k}+1) $end{document}</tex-math></inline-formula> is determined.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82158485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Security analysis of public key encryption with filtered equality test 带过滤等式检验的公钥加密安全性分析
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021053
Yu-Chi Chen
{"title":"Security analysis of public key encryption with filtered equality test","authors":"Yu-Chi Chen","doi":"10.3934/amc.2021053","DOIUrl":"https://doi.org/10.3934/amc.2021053","url":null,"abstract":"Public key encryption with equality test can provide a very simple add-on in which any one can directly perform testing over a pair of ciphertexts to check whether the underlying messages are identical or not without decryption. To restrict the such test power for different scenarios, that of delegated equality test is introduced to allow only the authenticated party to perform the test. In this paper, we focus on the security of public key encryption with filtered equality test (PKE-FET). The delegation to the party is only of a message set for designated testers in PKE-FET, which implies it cannot test any underlying message out of the set. We aim for investigating distinct security notions (static and adaptive security) with specific properties of the potential adversaries. Finally, we show the relationship between the security and complexity, and show the scheme of Huang et al. can reach adaptive security.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82260943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the correlation measures of orders $ 3 $ and $ 4 $ of binary sequence of period $ p^2 $ derived from Fermat quotients 由费马商导出周期$ p^2 $二元序列$ 3 $和$ 4 $阶的相关测度
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/AMC.2021008
Huaning Liu, Xi Liu
{"title":"On the correlation measures of orders $ 3 $ and $ 4 $ of binary sequence of period $ p^2 $ derived from Fermat quotients","authors":"Huaning Liu, Xi Liu","doi":"10.3934/AMC.2021008","DOIUrl":"https://doi.org/10.3934/AMC.2021008","url":null,"abstract":"Let begin{document}$ p $end{document} be a prime and let begin{document}$ n $end{document} be an integer with begin{document}$ (n, p) = 1 $end{document} . The Fermat quotient begin{document}$ q_p(n) $end{document} is defined as begin{document}$ q_p(n)equiv frac{n^{p-1}-1}{p} (bmod p), quad 0leq q_p(n)leq p-1. $end{document} We also define begin{document}$ q_p(kp) = 0 $end{document} for begin{document}$ kin mathbb{Z} $end{document} . Chen, Ostafe and Winterhof constructed the binary sequence begin{document}$ E_{p^2} = left(e_0, e_1, cdots, e_{p^2-1}right)in {0, 1}^{p^2} $end{document} as begin{document}$ begin{equation*} begin{split} e_{n} = left{begin{array}{ll} 0, & hbox{if } 0leq frac{q_p(n)}{p} and studied the well-distribution measure and correlation measure of order begin{document}$ 2 $end{document} by using estimates for exponential sums of Fermat quotients. In this paper we further study the correlation measures of the sequence. Our results show that the correlation measure of order begin{document}$ 3 $end{document} is quite good, but the begin{document}$ 4 $end{document} -order correlation measure of the sequence is very large.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76412079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A proof of the conjectured run time of the Hafner-McCurley class group algorithm Hafner-McCurley类群算法的推测运行时间证明
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021055
Jean-François Biasse, Muhammed Rashad Erukulangara
{"title":"A proof of the conjectured run time of the Hafner-McCurley class group algorithm","authors":"Jean-François Biasse, Muhammed Rashad Erukulangara","doi":"10.3934/amc.2021055","DOIUrl":"https://doi.org/10.3934/amc.2021055","url":null,"abstract":"<p style='text-indent:20px;'>We present a proof under a generalization of the Riemann Hypothesis that the class group algorithm of Hafner and McCurley runs in expected time <inline-formula><tex-math id=\"M1\">begin{document}$ e^{left(3/sqrt{8}+o(1)right)sqrt{log dloglog d}} $end{document}</tex-math></inline-formula> where <inline-formula><tex-math id=\"M2\">begin{document}$ -d $end{document}</tex-math></inline-formula> is the discriminant of the input imaginary quadratic order. In the original paper, an expected run time of <inline-formula><tex-math id=\"M3\">begin{document}$ e^{left(sqrt{2}+o(1)right)sqrt{log dloglog d}} $end{document}</tex-math></inline-formula> was proven, and better bounds were conjectured. To achieve a proven result, we rely on a mild modification of the original algorithm, and on recent results on the properties of the Cayley graph of the ideal class group.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87538930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On one-lee weight and two-lee weight $ mathbb{Z}_2mathbb{Z}_4[u] $ additive codes and their constructions 一元权$ mathbb{Z}_2mathbb{Z}_4[u] $加性码及其构造
IF 0.9 4区 计算机科学
Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI: 10.3934/amc.2021046
Jie Geng, Huazhang Wu, P. Solé
{"title":"On one-lee weight and two-lee weight $ mathbb{Z}_2mathbb{Z}_4[u] $ additive codes and their constructions","authors":"Jie Geng, Huazhang Wu, P. Solé","doi":"10.3934/amc.2021046","DOIUrl":"https://doi.org/10.3934/amc.2021046","url":null,"abstract":"<p style='text-indent:20px;'>This paper mainly study <inline-formula><tex-math id=\"M2\">begin{document}$ mathbb{Z}_{2}mathbb{Z}_{4}[u] $end{document}</tex-math></inline-formula>-additive codes. A Gray map from <inline-formula><tex-math id=\"M3\">begin{document}$ mathbb{Z}_{2}^{alpha}timesmathbb{Z}_{4}^{beta}[u] $end{document}</tex-math></inline-formula> to <inline-formula><tex-math id=\"M4\">begin{document}$ mathbb{Z}_{4}^{alpha+2beta} $end{document}</tex-math></inline-formula> is defined, and we prove that is a weight preserving and distance preserving map. A MacWilliams-type identity between the Lee weight enumerator of a <inline-formula><tex-math id=\"M5\">begin{document}$ mathbb{Z}_{2}mathbb{Z}_{4}[u] $end{document}</tex-math></inline-formula>-additive code and its dual is proved. Some properties of one-weight <inline-formula><tex-math id=\"M6\">begin{document}$ mathbb{Z}_{2}mathbb{Z}_{4}[u] $end{document}</tex-math></inline-formula>-additive codes and two-weight projective <inline-formula><tex-math id=\"M7\">begin{document}$ mathbb{Z}_{2}mathbb{Z}_{4}[u] $end{document}</tex-math></inline-formula>-additive codes are discussed. As main results, some construction methods for one-weight and two-weight <inline-formula><tex-math id=\"M8\">begin{document}$ mathbb{Z}_{2}mathbb{Z}_{4}[u] $end{document}</tex-math></inline-formula>-additive codes are studied, meanwhile several examples are presented to illustrate the methods.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90341350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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