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Riemann–Roch bases for Arbitrary Elliptic Curve Divisors and their Application in Cryptography
P. 1–5.
This paper presents explicit constructions of bases for Riemann-Roch spaces associated with arbitrary divisors on elliptic curves. In the context of algebraic geometry codes, the knowledge of an explicit basis for arbitrary divisors is especially valuable, as it enables efficient code construction. From a cryptographic point of view, codes associated with arbitrary divisors with many points are closer to Goppa codes, making them attractive for embedding in the McEliece cryptosystem. Using the results obtained in this work, it is also possible to efficiently construct quasi-cyclic subfield subcodes of elliptic codes. These codes enable a significant reduction in public key size for the McEliece cryptosystem and, consequently, represent promising candidates for integration into post-quantum codebased schemes.
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Zevakhina N., Щипкова А. А., Chinkova A., Voprosy Jazykoznanija 2025 No. 2 P. 105–122
This paper presents experimental evidence for the over-specification (redundant use) of Thai postnominal
numerals in referential communication. The first experiment reveals high rates of over-specification
in oral responses that include Thai postnominal and Russian prenominal numerals tested in a contrastive
multi-number visual context. The second experiment demonstrates lower but still relatively high
rates of over-specification in written responses that ...
Added: September 29, 2026
Kuninets A., Malygina E., Cryptography and Communications 2026 Vol. 18 No. 6 P. 2457–2497
In this paper, we determine explicit bases for Riemann–Roch spaces associated with various families of elliptic codes. We establish the feasibility and provide exact algorithms for constructing bases of Riemann–Roch spaces corresponding to arbitrary divisors on elliptic curves, including the non-effective case. These results are subsequently applied to derive bases for quasi-cyclic elliptic codes and ...
Added: September 17, 2026
Lebedev O. B., Лебедев Б. К., Известия ЮФУ. Технические науки 2026 № 2(250) С. 151–173
This paper proposes a methodology and method for constructing a model of the study area as a finite set of zones (sections) covering it, characterized by the fact that all sections are rectangular. The paper examines methods for forming a minimal set of sections on a large field that completely cover the accessible territory surveyed ...
Added: September 10, 2026
Kuninets A., Malygina E., Прикладная дискретная математика 2024 № 65 С. 84–109
Представлен обзор квазициклических альтернантных кодов и их структурный анализ относительно классификации автоморфизмов. Детализированы методы восстановления структурной информации о коде, которые, в свою очередь, снабжены подробными примерами. Привлекательность рассматриваемого семейства кодов заключается в его возможном криптографическом приложении и, как следствие, в уменьшении длины ключа постквантовых схем на кодах, исправляющих ошибки. К тому же данный метод построения ...
Added: December 12, 2025
Kuninets A., Прикладная дискретная математика. Приложение 2024 № 17 С. 147–152
Представлен обзор квазициклических альтернантных кодов и их структурный анализ относительно классификации автоморфизмов. Детализированы методы восстановления структурной информации о коде. Привлекательность рассматриваемого семейства кодов заключается в его возможном криптографическом приложении и, как следствие, в уменьшении длины ключа постквантовых схем на кодах, исправляющих ошибки. К тому же данный метод построения кодов является универсальным и может быть применён ...
Added: December 12, 2025
Dalian: IEEE, 2025.
The increasing complexity of modern software development necessitates intelligent, automated security analysis frameworks that can effectively pay attention of human on high-risk software releases. This paper introduces a Multi Agent System (MAS) framework designed to enhance the security assessment process by leveraging artificial intelligence (AI) and intelligent computing for real-time release analysis. The proposed system ...
Added: November 3, 2025
Kiritchenko V., Tsfasman M., Vladuts S. et al., Finite Fields and Their Applications 2025 Vol. 101 Article 102517
Quadratic residue patterns modulo a prime are studied since 19th century. In the first part we extend existing results on the number of consecutive ℓ-tuples of quadratic residues, studying corresponding algebraic curves and their Jacobians, which happen to be products of Jacobians of hyperelliptic curves. In the second part we state the last unpublished result of ...
Added: November 17, 2024
Sergeev A., Minchenkov V., Soldatov A., / Series Computer Science "arxiv.org". 2024. No. 2401.10777.
Systems of intelligent control of manual operations in industrial production are being implemented in many industries nowadays. Such systems use high-resolution cameras and computer vision algorithms to automatically track the operator's manipulations and prevent technological errors in the assembly process. At the same time compliance with safety regulations in the workspace is monitored. As a ...
Added: September 4, 2024
Якушенокс К. П., Ivanov F., / Series Computer Science "arxiv.org". 2023. No. 2312.15912.
Tavernier and Kabatiansky proposed new variants of the McEliece cryptosystem. In this letter, it is shown that cryptosystem based on correction of errors erasures is equal to the McEliece cryptosystem with worse parametrs public key. It will also add an organic extension of the authors’ idea, although one that has its flaws... ...
Added: September 4, 2024
M. N. Isaeva, A. A. Ovchinnikov, , in: 2023 Wave Electronics and its Application in Information and Telecommunication Systems (WECONF).: IEEE, 2023. P. 1–4.
Added: July 18, 2023
Kashtanov V., Reliability: Theory & Applications 2022 No. 4 P. 22–34
The article talks about a remarkable man and an outstanding scientist – Alexander Dmitrievich Soloviev. He was Doctor of Physics and Mathematics, Professor, Laureate of the State Prize of the USSR, Professor of the Probability Theory Department of the Faculty of Mechanics and Mathematics at Lomonosov Moscow State University. Alexander Dmitrievich lived an amazing creative ...
Added: February 3, 2023
Terry S. C., Ivanov F., Muhammad R. K. et al., Journal of Information Security and Applications 2023 Vol. 76 Article 103530
One main construct for code-based public key cryptosystems is the McEliece framework that hedges upon the hardness of decoding arbitrary linear codes. Based on Goppa codes, the original McEliece cryptosystem however, suffers from having very large public keys. To alleviate this problem, we define a new IKKR problem that is is NP-complete and use this assumption of the intracability if the ...
Added: December 28, 2022
Ivanova I., International Journal of General Systems 2022 Vol. 51 No. 7 P. 675–690
The paper focuses on the link between the dynamics of information and system evolution. Information, exchanged between different system’s parts, before being processed is first provided with meaning by the system. Meanings are generated from the perspective of hindsight, i.e. against the arrow of time. The same information can be differently interpreted by different system’s ...
Added: October 24, 2022
IEEE, 2020.
Proceedings of 2020 International Symposium on Information Theory and its Applications. ...
Added: November 2, 2021
Zevakhina N., Pasalskaya E., Chinkova A., Frontiers in Psychology 2021 Vol. 12 Article 745230
The paper presents experimental evidence for the over-specification of small cardinalities in reference 4 production. The first experiment shows that when presented with a small set (2, 3 or 4) of unique objects, 5 the speaker includes a numeral denoting a small cardinality into the description of given objects, although 6 it is over-informative for ...
Added: October 19, 2021
Guo D., Bai Y., Svinin M. et al., , in: 2022 International Siberian Conference on Control and Communications (SIBCON).: IEEE, 2022. Ch. 9438872 P. 1–5.
Added: October 11, 2021