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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., 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., Солдатов А. В., / 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
Bogomolov F. A., Fu H., European Journal of Mathematics 2020 Vol. 6 P. 1236–1253
Let E be an elliptic curve and 𝜋:𝐸→ℙ^1 a standard double cover identifying ±𝑃∈𝐸. It is known that for some torsion points 𝑃_𝑖 ∈ 𝐸, 1⩽𝑖⩽4, the cross ratio of {𝜋(𝑃𝑖)}^4_{𝑖=1} is independent of E. We will give a complete classification of such quadruples. ...
Added: October 10, 2021
IEEE, 2020.
Proceedings 2020 2nd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA). Lipetsk State Technical University Lipetsk, Russia November, 10-13 2020. Organized by Lipetsk State Technical University, Lipetsk, Russia. Technically Co-Sponsored by IEEE, IEEE Industrial Electronics Society (IES), IEEE Industry Applications Society, (IAS) Lipetsk State Technical Univ, STB ...
Added: June 17, 2021
Zhadnov V. V., Лукина А. С., Целищев И. С., Известия высших учебных заведений. Приборостроение 2021 Т. 64 № 9 С. 741–751
The paper deals with the issues of ensuring the operational dependability of modular power supply source by applying redundancy of their power channels. The subject of the study is the methods redundancy of power channels in modular power supply source. The purpose of the work is to improve the quality of design of redundant modular ...
Added: April 22, 2021
Pavlov A., Mathematische Zeitschrift 2021 No. 297 P. 223–254
We show that for maximal Cohen–Macaulay modules over the homogeneous coordinate ring of a smooth Calabi–Yau varieties X, the computation of Betti numbers can be reduced to computations of dimensions of certain HomHom spaces in the bounded derived category Db(X). In the simplest case of a smooth elliptic curve E embedded in P2 as a smooth cubic, we get explicit values for Betti ...
Added: October 31, 2020
Ivanov F., Krouk E., Kabatiansky G., , in: Code-Based Cryptography. CBCrypto 2020.: Springer, 2020. Ch. 3 P. 41–49.
Unlike most papers devoted to improvements of code-based cryptosystem, where original Goppa codes are substituted by some other codes, we suggest a new method of strengthening which is code-independent. We show (up to some limit) that the security of the new code-based cryptosystem is much closer to the hardness of maximum likelihood decoding than in the ...
Added: October 26, 2020
IEEE, 2020.
Added: October 22, 2020
Zhadnov V. V., Polesskiy S., Russian Electrical Engineering 2020 Vol. 91 No. 7 P. 262–267
One promising trend in making voltage converters more reliable is to design them on the basis of backbone modular architecture, combined redundancy, and rotation of main and backup power channels. A technique is proposed for this converter for calculating the upper and the lower failsafe operation probability estimates that is based on using the standardized ...
Added: October 19, 2020
Gribkova Nadezhda, Journal of Statistics and Management System ISSN 0972-0510 (Print), ISSN 2169-0014 (Online) Taylor & Francis 2020 Vol. 23 No. 8 P. 1285–1304
Control systems are exposed to unintentional errors, deliberate intrusions, false data injection attacks, and various other disruptions. In this paper we propose, justify, and illustrate a rule of thumb for detecting, or confirming the absence of, such disruptions. To facilitate the use of the rule, we rigorously discuss underlying results that delineate the boundaries of the rule’s applicability. We ...
Added: October 17, 2020