Pub Date : 2023-11-03DOI: 10.1142/s0219498825300028
Luciano Maino, Marzio Mula, Federico Pintore
CSIDH is a post-quantum key-exchange scheme based on the action of ideal class groups on supersingular elliptic curves over prime fields. Its short keys and ciphertexts, together with its flexibility as a building block to construct complex cryptographic primitives, has motivated significant research on the efficiency of CSIDH and its resistance against side-channel attacks. In this work, some cutting-edge results from recent contributions are reviewed in a unified treatment, focusing on the mathematical ideas lying behind them rather than on cryptographic and low-level implementation techniques. In particular, we first describe ways to speed up the class-group-action evaluation, which range from the use of different models of elliptic curves to working with different ideal class groups. We then survey some constant-time variants of CSIDH, that make the time and memory consumption during the computation of a public/shared key independent of the secret key. Finally, we examine the computation of the ideal class action when the structure of the ideal class group is known, which is the case for a specific set of CSIDH parameters.
{"title":"A Review of Mathematical and Computational Aspects of CSIDH Algorithms","authors":"Luciano Maino, Marzio Mula, Federico Pintore","doi":"10.1142/s0219498825300028","DOIUrl":"https://doi.org/10.1142/s0219498825300028","url":null,"abstract":"CSIDH is a post-quantum key-exchange scheme based on the action of ideal class groups on supersingular elliptic curves over prime fields. Its short keys and ciphertexts, together with its flexibility as a building block to construct complex cryptographic primitives, has motivated significant research on the efficiency of CSIDH and its resistance against side-channel attacks. In this work, some cutting-edge results from recent contributions are reviewed in a unified treatment, focusing on the mathematical ideas lying behind them rather than on cryptographic and low-level implementation techniques. In particular, we first describe ways to speed up the class-group-action evaluation, which range from the use of different models of elliptic curves to working with different ideal class groups. We then survey some constant-time variants of CSIDH, that make the time and memory consumption during the computation of a public/shared key independent of the secret key. Finally, we examine the computation of the ideal class action when the structure of the ideal class group is known, which is the case for a specific set of CSIDH parameters.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"182 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775740","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}
Pub Date : 2023-11-03DOI: 10.1142/s021949882550094x
Huihui Zheng, Linlin Liu
In this paper, firstly, we introduce the notion of matching Rota–Baxter modules, which generalizes the notions of matching Rota–Baxter algebras and Rota–Baxter modules, and give its characteristic and construction. Secondly, we give the relation between matching Rota–Baxter modules and other modules structure. Finally, we introduce the notion of matching [Formula: see text]-operators of associative algebras which also generalizes the notion of matching Rota–Baxter algebras and give the solution of polarized associative Yang–Baxter equation by using the matching [Formula: see text]-operators of associative algebras. In addition, we introduce the definitions of the compatible matching [Formula: see text]-operators of associative algebras, matching Nijenhui operators, and compatible matching dendriform algebras, and consider their connection.
{"title":"Matching Rota-Baxter modules and Matching 𝒪-operators of associative algebras","authors":"Huihui Zheng, Linlin Liu","doi":"10.1142/s021949882550094x","DOIUrl":"https://doi.org/10.1142/s021949882550094x","url":null,"abstract":"In this paper, firstly, we introduce the notion of matching Rota–Baxter modules, which generalizes the notions of matching Rota–Baxter algebras and Rota–Baxter modules, and give its characteristic and construction. Secondly, we give the relation between matching Rota–Baxter modules and other modules structure. Finally, we introduce the notion of matching [Formula: see text]-operators of associative algebras which also generalizes the notion of matching Rota–Baxter algebras and give the solution of polarized associative Yang–Baxter equation by using the matching [Formula: see text]-operators of associative algebras. In addition, we introduce the definitions of the compatible matching [Formula: see text]-operators of associative algebras, matching Nijenhui operators, and compatible matching dendriform algebras, and consider their connection.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"179 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775418","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}
Pub Date : 2023-11-03DOI: 10.1142/s0219498825501336
Fernando Sancho De Salas
{"title":"Cohomology of Partially Ordered Sets and Ext's","authors":"Fernando Sancho De Salas","doi":"10.1142/s0219498825501336","DOIUrl":"https://doi.org/10.1142/s0219498825501336","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"99 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869151","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}
Pub Date : 2023-11-02DOI: 10.1142/s021949882550063x
Markus Grassl, Anna-Lena Horlemann, Violetta Weger
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes. We set up the theoretic framework for this weight and metric, including upper and lower bounds, asymptotic behavior of random codes, and we show the existence of an optimal family of codes achieving the Singleton-type upper bound.
{"title":"The Subfield Metric and its Application to Quantum Error Correction","authors":"Markus Grassl, Anna-Lena Horlemann, Violetta Weger","doi":"10.1142/s021949882550063x","DOIUrl":"https://doi.org/10.1142/s021949882550063x","url":null,"abstract":"We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric quantum codes. We set up the theoretic framework for this weight and metric, including upper and lower bounds, asymptotic behavior of random codes, and we show the existence of an optimal family of codes achieving the Singleton-type upper bound.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"64 17","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135874433","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}
Pub Date : 2023-11-01DOI: 10.1142/s021949882550080x
Chris Monico
In [D. R. L. Brown, Plactic key agreement (insecure?), J. Math. Cryptol. 17(1) (2023) 20220010], a novel cryptographic key exchange technique was proposed using the plactic monoid, based on the apparent difficulty of solving division problems in that monoid. Specifically, given elements [Formula: see text] in the plactic monoid, the problem is to find [Formula: see text] for which [Formula: see text], given that such a [Formula: see text] exists. In this paper, we introduce a metric on the plactic monoid and use it to give a probabilistic algorithm for solving that problem which is fast for parameter values in the range of interest.
在[D。R. L. Brown, Plactic key agreement (insecure?)， J. Math。Cryptol. 17(1)(2023) 20220010]，基于求解plactic单群中除法问题的明显困难，提出了一种新的加密密钥交换技术。具体地说，给定plactic monooid中的元素[Formula: see text]，问题是找到[Formula: see text]的[Formula: see text]，假设存在这样一个[Formula: see text]。在本文中，我们引入了一个关于plactic monooid的度量，并利用它给出了一个求解该问题的概率算法，该算法对于参数值在感兴趣的范围内是快速的。
{"title":"Division in the Plactic Monoid","authors":"Chris Monico","doi":"10.1142/s021949882550080x","DOIUrl":"https://doi.org/10.1142/s021949882550080x","url":null,"abstract":"In [D. R. L. Brown, Plactic key agreement (insecure?), J. Math. Cryptol. 17(1) (2023) 20220010], a novel cryptographic key exchange technique was proposed using the plactic monoid, based on the apparent difficulty of solving division problems in that monoid. Specifically, given elements [Formula: see text] in the plactic monoid, the problem is to find [Formula: see text] for which [Formula: see text], given that such a [Formula: see text] exists. In this paper, we introduce a metric on the plactic monoid and use it to give a probabilistic algorithm for solving that problem which is fast for parameter values in the range of interest.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"161 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135011744","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}
Pub Date : 2023-11-01DOI: 10.1142/s0219498825500902
Kamal Paykan, Mohammad Habibi
In this paper, we continue to study skew inverse Laurent series ring [Formula: see text], where [Formula: see text] is a ring equipped with an automorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. We directly prove that [Formula: see text] is semiprimitive reduced if and only if [Formula: see text] is [Formula: see text]-rigid. Also, as an application of our results, by imposing constraints on [Formula: see text] and [Formula: see text], we completely identify the Jacobson radical of [Formula: see text] whose set of all nilpotent elements has special conditions. Moreover, necessary and sufficient conditions are obtained for the skew inverse Laurent series ring to satisfy a certain ring property which is among being right Artinian, completely primary, right perfect, (semi)local, semiperfect, semiprimary, semiregular, semisimple and strongly regular, respectively.
{"title":"An Alternative Perspective on Jacobson Radical of Skew Inverse Laurent Series Rings","authors":"Kamal Paykan, Mohammad Habibi","doi":"10.1142/s0219498825500902","DOIUrl":"https://doi.org/10.1142/s0219498825500902","url":null,"abstract":"In this paper, we continue to study skew inverse Laurent series ring [Formula: see text], where [Formula: see text] is a ring equipped with an automorphism [Formula: see text] and an [Formula: see text]-derivation [Formula: see text]. We directly prove that [Formula: see text] is semiprimitive reduced if and only if [Formula: see text] is [Formula: see text]-rigid. Also, as an application of our results, by imposing constraints on [Formula: see text] and [Formula: see text], we completely identify the Jacobson radical of [Formula: see text] whose set of all nilpotent elements has special conditions. Moreover, necessary and sufficient conditions are obtained for the skew inverse Laurent series ring to satisfy a certain ring property which is among being right Artinian, completely primary, right perfect, (semi)local, semiperfect, semiprimary, semiregular, semisimple and strongly regular, respectively.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"91 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135012039","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}
Pub Date : 2023-11-01DOI: 10.1142/s0219498825500872
Hani Abdelwahab, Amir Fernandez Ouaridi, Candido Martin Gonzalez
We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the [Formula: see text]-dimensional Poisson algebras. In addition, we study the geometric classification, the graph of degenerations and the closures of the orbits of the variety of [Formula: see text]-dimensional Poisson algebras. Finally, we also study the algebraic classification of the Poisson algebras defined on a commutative associative null-filiform or filiform algebra and, to enrich this classification, we study the degenerations between these particular Poisson algebras.
{"title":"Degenerations of Poisson Algebras","authors":"Hani Abdelwahab, Amir Fernandez Ouaridi, Candido Martin Gonzalez","doi":"10.1142/s0219498825500872","DOIUrl":"https://doi.org/10.1142/s0219498825500872","url":null,"abstract":"We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the [Formula: see text]-dimensional Poisson algebras. In addition, we study the geometric classification, the graph of degenerations and the closures of the orbits of the variety of [Formula: see text]-dimensional Poisson algebras. Finally, we also study the algebraic classification of the Poisson algebras defined on a commutative associative null-filiform or filiform algebra and, to enrich this classification, we study the degenerations between these particular Poisson algebras.","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"269 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135011792","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}
Pub Date : 2023-10-31DOI: 10.1142/s0219498825501269
Adel Alahmadi, Asmaa Melaibari, Patrick Sole
{"title":"Self-orthogonal codes over a non-unital ring from two class association schemes","authors":"Adel Alahmadi, Asmaa Melaibari, Patrick Sole","doi":"10.1142/s0219498825501269","DOIUrl":"https://doi.org/10.1142/s0219498825501269","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"27 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135863382","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}
Pub Date : 2023-10-31DOI: 10.1142/s0219498825501312
Viviana Gubitosi, Rafael Parra
{"title":"Finiteness Properties and Homological Dimensions of Skew Group Rings","authors":"Viviana Gubitosi, Rafael Parra","doi":"10.1142/s0219498825501312","DOIUrl":"https://doi.org/10.1142/s0219498825501312","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135870011","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}
Pub Date : 2023-10-31DOI: 10.1142/s0219498825501294
Pjek-Hwee Lee
{"title":"On Quasi-Duo Differential Polynomial Rings","authors":"Pjek-Hwee Lee","doi":"10.1142/s0219498825501294","DOIUrl":"https://doi.org/10.1142/s0219498825501294","url":null,"abstract":"","PeriodicalId":54888,"journal":{"name":"Journal of Algebra and Its Applications","volume":"72 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135863094","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}
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