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A New Code-Based Cryptosystem
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 original McEliece cryptosystem.
In book
Ivanov F., Krouk E., Kabatiansky G. A., Rumenko N. Springer, 2020.
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
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
Kuninets A., Malygina E., , in: 2025 XIХ International Symposium on Problems of Redundancy in Information and Control Systems (Redundancy), 5-7 Nov. 2025.: IEEE, 2025. 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 ...
Added: December 29, 2025
Исаева М. Н., Научно-технический вестник информационных технологий, механики и оптики 2025 Т. 25 № 2 С. 286–294
When transmitting information over channels with grouping errors, the traditional approach is channel decorrelation and use of codes correcting independent errors. The decorrelation procedure lowers achievable rates of reliable transmission, therefore the problem of using special codes for channels with memory and construction of computationally effective decoding methods for correction of grouping errors is actual. ...
Added: September 18, 2025
Alina M. Veresova, Andrei A. Ovchinnikov, , in: 2024 IEEE 3rd International Conference on Problems of Informatics, Electronics and Radio Engineering (PIERE).: IEEE, 2024. P. 1130–1134.
The article discusses the data transmission using convolutional codes over channels where the noise process can be described by a Markov chain with two states: a simple binary Markov channel and the Gilbert channel. Using the classical Viterbi algorithm with the Hamming metric for these channels does not guarantee low error probabilities. Additionally, the use ...
Added: May 14, 2025
Kabatiansky G. A., Evgenii A. Krouk, , in: 2024 IEEE International Multi-Conference on Engineering, Computer and Information Sciences (SIBIRCON).: Novosibirsk: IEEE, 2024. P. 85–88.
A new approach to code-based cryptosystems is pro-posed that extends the classical McEliece cryptosystem because its public code is not equivalent to a secret code, as well as a non-trivial linear transformation of the error vector is used. Moreover, in the new system, legal users decipher secret messages via correction t′ errors and S erasures, while illegal users must ...
Added: December 12, 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
Ivanov F., Kuvshinov A., , in: Proceedings of VII International Conference «Engineering & Telecommunication — En&T-2021.: IEEE, 2021. P. 1–5.
Added: June 1, 2024
Исаева М. Н., Ovchinnikov A., Научно-технический вестник информационных технологий, механики и оптики 2024 Т. 24 № 1 С. 70–80
The most important method of ensuring data integrity is correcting errors that occur during information storage,
processing or transmission. The error-correcting coding methods are used to correct errors. In real systems, noise
processes are correlated. However, traditional coding and decoding methods use decorrelation, and it is known that
this procedure reduces the maximum achievable characteristics of coding. Thus, ...
Added: March 4, 2024
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
Zyablov V., Ivanov F., Krouk E. et al., Problems of Information Transmission 2022 Vol. 58 No. 2 P. 184–201
We consider the problem of constructing a cryptosystem with a public key based on error-resistant coding. At present, this type of cryptosystems is believed to be able to resist the advent of quantum computers and can be considered as a method of post-quantum cryptography. The main drawback of a code-based cryptosystem is a great length ...
Added: October 26, 2022
Ivanov F., Krouk E., Zyablov V., , in: 2021 XVII International Symposium "Problems of Redundancy in Information and Control Systems" (REDUNDANCY).: IEEE, 2021.
McEliece cryptosystem represents a smart open key
system based on the hardness of the decoding of an arbitrary
linear code, which is believed to be able to resist the advent
of quantum computers. But the original McEliece cryptosystem,
based on Goppa codes, has just very limited interest in practice,
partly because it requires a very large public key. In this ...
Added: November 30, 2021
Ivanov F., Krouk E., Kabatiansky G. A. et al., Lecture Notes in Computer Science 2020 Vol. 12087 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: September 17, 2020
Ivanov F., Krouk E., Kabatiansky G. A. et al., Springer, 2020.
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: September 17, 2020