Structure of quaternion-type algebras and a post-quantum signature algorithm.
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| Title: | Structure of quaternion-type algebras and a post-quantum signature algorithm. |
|---|---|
| Authors: | May Thu Duong1 dtmay@ictu.edu.vn, Moldovyan, Alexander Andreevich2 maa1305@yandex.ru, Moldovyan, Dmitriy Nikolaevich2 mdn.spectr@mail.ru, Minh Hieu Nguyen3 hieuminhmta@gmail.com, Bac Thi Do4 dtbac@ictu.edu.vn |
| Source: | International Journal of Electrical & Computer Engineering (2088-8708). Jun2025, Vol. 15 Issue 3, p2965-2976. 12p. |
| Subjects: | Commutative algebra, Noncommutative algebras, Digital signatures, Abelian groups, Internet of things |
| Abstract: | Algebraic digital signature algorithms with a commutative hidden group, which are based on the computational difficulty of solving large systems of power equations, are promising candidates for post-quantum cryptoschemes, especially in securing applications like the internet of things (IoT) and other information technologies. Associative finite non-commutative algebras are used as an algebraic support of the said algorithms. Among such algebras, finite quaternion-type algebras have been identified as strong candidates for providing algebraic support. This paper investigates the decomposition of these algebras into commutative subrings and explores their multiplicative groups, which can serve as potential hidden groups. The analysis reveals the existence of three distinct types of subrings, with derived formulas for the number of subrings and the orders of their multiplicative groups. These findings align with previous studies on fourdimensional algebras defined by sparse basis vector multiplication tables. Using the finite quaternion-type algebras as algebraic support, a novel post-quantum signature algorithm characterized in using two mutually non-commutative hidden groups has been developed. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Electrical & Computer Engineering (2088-8708) is the property of Institute of Advanced Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 186514249 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Structure of quaternion-type algebras and a post-quantum signature algorithm. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22May+Thu+Duong%22">May Thu Duong</searchLink><relatesTo>1</relatesTo><i> dtmay@ictu.edu.vn</i><br /><searchLink fieldCode="AR" term="%22Moldovyan%2C+Alexander+Andreevich%22">Moldovyan, Alexander Andreevich</searchLink><relatesTo>2</relatesTo><i> maa1305@yandex.ru</i><br /><searchLink fieldCode="AR" term="%22Moldovyan%2C+Dmitriy+Nikolaevich%22">Moldovyan, Dmitriy Nikolaevich</searchLink><relatesTo>2</relatesTo><i> mdn.spectr@mail.ru</i><br /><searchLink fieldCode="AR" term="%22Minh+Hieu+Nguyen%22">Minh Hieu Nguyen</searchLink><relatesTo>3</relatesTo><i> hieuminhmta@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Bac+Thi+Do%22">Bac Thi Do</searchLink><relatesTo>4</relatesTo><i> dtbac@ictu.edu.vn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Electrical+%26+Computer+Engineering+%282088-8708%29%22">International Journal of Electrical & Computer Engineering (2088-8708)</searchLink>. Jun2025, Vol. 15 Issue 3, p2965-2976. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Commutative+algebra%22">Commutative algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Noncommutative+algebras%22">Noncommutative algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Digital+signatures%22">Digital signatures</searchLink><br /><searchLink fieldCode="DE" term="%22Abelian+groups%22">Abelian groups</searchLink><br /><searchLink fieldCode="DE" term="%22Internet+of+things%22">Internet of things</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Algebraic digital signature algorithms with a commutative hidden group, which are based on the computational difficulty of solving large systems of power equations, are promising candidates for post-quantum cryptoschemes, especially in securing applications like the internet of things (IoT) and other information technologies. Associative finite non-commutative algebras are used as an algebraic support of the said algorithms. Among such algebras, finite quaternion-type algebras have been identified as strong candidates for providing algebraic support. This paper investigates the decomposition of these algebras into commutative subrings and explores their multiplicative groups, which can serve as potential hidden groups. The analysis reveals the existence of three distinct types of subrings, with derived formulas for the number of subrings and the orders of their multiplicative groups. These findings align with previous studies on fourdimensional algebras defined by sparse basis vector multiplication tables. Using the finite quaternion-type algebras as algebraic support, a novel post-quantum signature algorithm characterized in using two mutually non-commutative hidden groups has been developed. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Electrical & Computer Engineering (2088-8708) is the property of Institute of Advanced Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.11591/ijece.v15i3.pp2965-2976 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 2965 Subjects: – SubjectFull: Commutative algebra Type: general – SubjectFull: Noncommutative algebras Type: general – SubjectFull: Digital signatures Type: general – SubjectFull: Abelian groups Type: general – SubjectFull: Internet of things Type: general Titles: – TitleFull: Structure of quaternion-type algebras and a post-quantum signature algorithm. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: May Thu Duong – PersonEntity: Name: NameFull: Moldovyan, Alexander Andreevich – PersonEntity: Name: NameFull: Moldovyan, Dmitriy Nikolaevich – PersonEntity: Name: NameFull: Minh Hieu Nguyen – PersonEntity: Name: NameFull: Bac Thi Do IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 20888708 Numbering: – Type: volume Value: 15 – Type: issue Value: 3 Titles: – TitleFull: International Journal of Electrical & Computer Engineering (2088-8708) Type: main |
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