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Semidirect Product Key Exchange: the State of Play 半直接产品密钥交换:游戏状态
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-27 DOI: 10.1142/s0219498825500665
Christopher Battarbee, Delaram Kahrobaei, Siamak F. Shahandashti
{"title":"Semidirect Product Key Exchange: the State of Play","authors":"Christopher Battarbee, Delaram Kahrobaei, Siamak F. Shahandashti","doi":"10.1142/s0219498825500665","DOIUrl":"https://doi.org/10.1142/s0219498825500665","url":null,"abstract":"Of the many families of cryptographic schemes proposed to be post-quantum, a relatively unexplored set of examples comes from group-based cryptography. One of the more central schemes from this area is the so-called Semidirect Product Key Exchange (SDPKE), a generalization of Diffie–Hellman Key Exchange that is plausibly post-quantum. In this report we survey the state of the literature relating to SDPKE, providing a high-level discussion of security, as well as a comprehensive overview of the proposed platforms and the main cryptanalytic ideas relevant to each.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"22 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Abundance and magnifying elements in transformation semigroups that preserve order and equivalence 保持序和等价的变换半群中的丰度和放大元素
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-27 DOI: 10.1142/s0219498825501208
Lei Sun
{"title":"Abundance and magnifying elements in transformation semigroups that preserve order and equivalence","authors":"Lei Sun","doi":"10.1142/s0219498825501208","DOIUrl":"https://doi.org/10.1142/s0219498825501208","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"148 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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 existence of sympathetic lie algebras with dimension less than 25 关于维数小于25的交感李代数的存在性
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-27 DOI: 10.1142/s0219498825501221
A. L. Garcia-Pulido, G. Salgado
{"title":"On the existence of sympathetic lie algebras with dimension less than 25","authors":"A. L. Garcia-Pulido, G. Salgado","doi":"10.1142/s0219498825501221","DOIUrl":"https://doi.org/10.1142/s0219498825501221","url":null,"abstract":"In this article we investigate the question of the lowest possible dimension that a sympathetic Lie algebra $mathfrak{g}$ can attain, when its Levi subalgebra $mathfrak{g}_L$ is simple. We establish the structure of the nilradical of a perfect Lie algebra $mathfrak{g}$, as a $mathfrak{g}_L$-module, and determine the possible Lie algebra structures that one such $mathfrak{g}$ admits. We prove that, as a $mathfrak{g}_L$-module, the nilradical must decompose into at least 4 simple modules. We explicitly calculate the semisimple derivations of a perfect Lie algebra $mathfrak{g}$ with Levi subalgebra $mathfrak{g}_L = mathfrak{sl}_2(mathbb{C})$ and give necessary conditions for $mathfrak{g}$ to be a sympathetic Lie algebra in terms of these semisimple derivations. We show that there is no sympathetic Lie algebra of dimension lower than 15, independently of the nilradical's decomposition. If the nilradical has 4 simple modules, we show that a sympathetic Lie algebra has dimension greater or equal than 25.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"18 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
q-crossed modules and q-capability of Lie algebras 李代数的q-交叉模与q-能力
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-27 DOI: 10.1142/s0219498825501233
Emzar Khmaladze, Manuel Ladra
{"title":"<i>q</i>-crossed modules and <i>q</i>-capability of Lie algebras","authors":"Emzar Khmaladze, Manuel Ladra","doi":"10.1142/s0219498825501233","DOIUrl":"https://doi.org/10.1142/s0219498825501233","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"15 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Remarks on the Dual Notion of n-Absorbing Primary Submodules 关于n吸收主子模对偶概念的若干注释
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-20 DOI: 10.1142/s0219498825500860
F. Ranjbar Hamghavandi, M. Ebrahimpour
{"title":"Some Remarks on the Dual Notion of <i>n</i>-Absorbing Primary Submodules","authors":"F. Ranjbar Hamghavandi, M. Ebrahimpour","doi":"10.1142/s0219498825500860","DOIUrl":"https://doi.org/10.1142/s0219498825500860","url":null,"abstract":"Let [Formula: see text] be a positive integer. In this paper, we introduce a functional method, which gives us an equivalent condition to the concept of [Formula: see text]-absorbing primary submodules. By using this method, the dual notion of [Formula: see text]-absorbing primary submodules, which we call [Formula: see text]-secondary submodules, is presented. Then, some properties of this class of submodules, several useful examples and functorial results are presented.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finite groups with integer harmonic mean of element orders 具有元阶整数调和平均值的有限群
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-20 DOI: 10.1142/s0219498825500835
Iulia Catalina Plesca, Marius Tarnauceanu
{"title":"Finite groups with integer harmonic mean of element orders","authors":"Iulia Catalina Plesca, Marius Tarnauceanu","doi":"10.1142/s0219498825500835","DOIUrl":"https://doi.org/10.1142/s0219498825500835","url":null,"abstract":"In this paper, we introduce a new function computing the harmonic mean of element orders of a finite group. We present a series of properties for this function, and then we study groups for which the value of the function is an integer.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"15 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Resolving subcategories and singularity categories 解析子类别和奇异类别
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-20 DOI: 10.1142/s0219498825501142
Nan Gao, Keyan Song, Hanyang You, Guodong Zhou
{"title":"Resolving subcategories and singularity categories","authors":"Nan Gao, Keyan Song, Hanyang You, Guodong Zhou","doi":"10.1142/s0219498825501142","DOIUrl":"https://doi.org/10.1142/s0219498825501142","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectra of Zero-Divisor Graphs of Finite Reduced Rings 有限约简环的零因子图的谱
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-20 DOI: 10.1142/s0219498825500823
Gahininath Sonawane, Ganesh S. Kadu, Y. M. Borse
{"title":"Spectra of Zero-Divisor Graphs of Finite Reduced Rings","authors":"Gahininath Sonawane, Ganesh S. Kadu, Y. M. Borse","doi":"10.1142/s0219498825500823","DOIUrl":"https://doi.org/10.1142/s0219498825500823","url":null,"abstract":"Let [Formula: see text] be a finite reduced ring with [Formula: see text] maximal ideals [Formula: see text] and let [Formula: see text] be the zero-divisor graph associated to [Formula: see text] The class of rings [Formula: see text] contains the Boolean rings as a subclass. When [Formula: see text] for all [Formula: see text] where [Formula: see text] is a finite field, we associate two [Formula: see text] sized matrices [Formula: see text] and [Formula: see text] to the graph [Formula: see text] having combinatorial entries and use these matrices to determine the spectrum of this graph. More precisely, we show that every eigenvalue of [Formula: see text] and of [Formula: see text] is an eigenvalue of [Formula: see text] To do this, we give a recursive description of the adjacency matrix of this graph and also exhibit its equitable partition. This is used in computing the determinant, rank and nullity of the adjacency matrix. Further, we propose that the eigenvalues of [Formula: see text] [Formula: see text] and the eigenvalue [Formula: see text] exhaust all the eigenvalues of [Formula: see text]","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp Permutation Groups Whose Point Stabilizers are AGL(1,p) 点稳定器为AGL(1,p)的锐置换群
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-20 DOI: 10.1142/s0219498825501178
Blake Norman
{"title":"Sharp Permutation Groups Whose Point Stabilizers are AGL(1,<i>p</i>)","authors":"Blake Norman","doi":"10.1142/s0219498825501178","DOIUrl":"https://doi.org/10.1142/s0219498825501178","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"3 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gorenstein AC-Projective and AC-Injective Representations of Quivers 颤颤子的ac -射影和ac -内射表示
3区 数学
Journal of Algebra and Its Applications Pub Date : 2023-10-20 DOI: 10.1142/s0219498825501191
Dejun Wu, Hui Zhou, Yongduo Wang
{"title":"Gorenstein AC-Projective and AC-Injective Representations of Quivers","authors":"Dejun Wu, Hui Zhou, Yongduo Wang","doi":"10.1142/s0219498825501191","DOIUrl":"https://doi.org/10.1142/s0219498825501191","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135566619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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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