Code-based public-key cryptosystems for the post-quantum period

Kuznetsov, Alexandr; Svatovskij, Igor; Kiyan, Nastya; Pushkar'ov, Andriy

doi:10.1109/infocommst.2017.8246365

Cited by 41 publications

(14 citation statements)

References 37 publications

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“…These results may also be useful in other important practical applications: cryptography, authentication, the theory of complex signals, etc. [14][15][16].…”

Section: Discussionmentioning

confidence: 99%

“…α16 , α 32 ,(63, 36,11) α3 , α6 , α12 , α 24 , α 48 , α 33 ,α 5 , α 10 , α 20 , α 40 , α 17 , α 34 , α 7 , α 14 , α 28 , α 56 , α 49 , α 35 , α 9 , α 18 , α 36 GF (2 7 ) α 1 , α 2 , α 4 , α 8 , α 16 , α 32 , α 64 , (127, 64, 21) α 3 , α 6 , α 12 , α 24 , α 48 , α 96 , α 65 , α 5 , α 10 , α 20 , α 40 , α 80 , α 33 , α 66 , α 7 , α14 , α 28 , α 56 , α 112 , α 97 , α 67 , α 9 , α 18 , α 36 , α 72 , α 17 , α 34 , α 68 , α 11 , α 22 , α 44 , α 88 , α 49 , α 98 , α 69 , α 13 , α 26 , α 52 , α 104 , α 81 , α 35 , α 70 , α 15 , α 30 , α 60 , α 120 , α 113 , α 99 , α 71 , α 19 , α 38 , α 76 , α 25 , α 50 , α 100 , α 73 Primitive binary BCH-code.…”

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Energy Gain From Error-Correcting Coding in Channels With Grouping Errors

2020

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Abstract. This article explores the a mathematical model of the a data transmission channel with errors grouping. We propose an estimating method for energy gain from coding and energy efficiency of binary codes in channels with grouped errors. The proposed method uses a simplified Bennet and Froelich’s model and allows leading the research of the energy gain from coding for a wide class of data channels without restricting the way of the length distributing the error bursts. The reliability of the obtained results is confirmed by the information of the known results in the theory of error-correcting coding in the simplified variant.

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“…These results may also be useful in other important practical applications: cryptography, authentication, the theory of complex signals, etc. [14][15][16].…”

Section: Discussionmentioning

confidence: 99%

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Energy Gain From Error-Correcting Coding in Channels With Grouping Errors

2020

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“…The constant-weight codes are also useful to perform the operation of code-based cryptosystems [9][10][11][12][13][14][15][16][17][18]. In particular, they are used in McEliece [9] and Niederreiter [10] public key encryption systems, as well as in electronic signature schemes [13,14] and pseudo-random number generators [11,12].…”

Section: Introductionmentioning

confidence: 99%

Full Non-Binary Constant-Weight Codes

et al. 2021

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This paper presents the research results of mixed base number systems using binomial representation of numbers. It also shows the investigated non-linear coding techniques with full constant-weight codes, which are based on the binomial numeration. These codes can be used in a variety of computer applications: in code-based cryptosystems; to detect errors in asymmetric communication channels, etc. We propose a new numeral system. It combines the features of positional and binomial numeration. We suggest a technique of full non-binary constant-weight coding based on a generalized binomialpositional representation. It allows us to generalize the known approach to the non-binary case and practically implement computational algorithms for generating full set of non-binary constant-weight sequences. There are the analytical relations that relate the positional and binomial representations of numbers. The article provides several examples, which clear up the usefulness and the constructiveness of the proposed approach, and simplify the perception and understanding of results. We also consider some aspects of the potential use of the proposed numeral system. In particular, the article discusses asymmetric communication channels (the model of a binary Z-channel and its generalization to the non-binary model), and shows the advantage of constant-weight codes for error detection.

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“…There are two major classes of methods to replace traditional cryptographythe first one is quantum cryptography (QC) [1], based on the fundamental difference, the use of the unique capabilities of quantum mechanics; the second is post-quantum cryptography (PQC) [2], based on the more complicated mathematical problems (for example, lattice-based cryptosystems, syndrome-based cryptosystems and others).…”

Section: Introductionmentioning

confidence: 99%

High-Speed and Secure PRNG for Cryptographic Applications

Hu¹,

Gnatyuk²,

Okhrimenko³

et al. 2020

IJCNIS

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Due to the fundamentally different approach underlying quantum cryptography (QC), it has not only become competitive, but also has significant advantages over traditional cryptography methods. Such significant advantage as theoretical and informational stability is achieved through the use of unique quantum particles and the inviolability of quantum physics postulates, in addition it does not depend on the intruder computational capabilities. However, even with such impressive reliability results, QC methods have some disadvantages. For instance, such promising trend as quantum secure direct communicationeliminates the problem of key distribution, since it allows to transmit information by open channel without encrypting it. However, in these protocols, each bit is confidential and should not be compromised, therefore, the requirements for protocol stability are increasing and additional security methods are needed. For a whole class of methods to ensure qutrit QC protocols stability, reliable trit generation method is required. In this paper authors have developed and studied trit generation method and software tool TriGen v.2.0 PRNG. Developed PRNG is important for various practical cryptographic applications (for example, trit QC systems, IoT and Blockchain technologies). Future research can be related with developing fully functional version of testing technique and software tool.

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Code-based public-key cryptosystems for the post-quantum period

Cited by 41 publications

References 37 publications

Energy Gain From Error-Correcting Coding in Channels With Grouping Errors

Energy Gain From Error-Correcting Coding in Channels With Grouping Errors

Full Non-Binary Constant-Weight Codes

High-Speed and Secure PRNG for Cryptographic Applications

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