Public-key code-based cryptography
DOI:
https://doi.org/10.18372/2410-7840.18.11088Keywords:
code-Based Cryptosystems, post-quantum cryptographyAbstract
The possibility of a quantum computer threatens the existence of many asymmetric cryptographic primitives. An important advantage of code cryptosystems is the high resistance to the quantum cryptanalysis. Therefore it is in great demand increasing the speed of the code based primitives and their protection from classical cryptanalysis. Code-Based Public-Key Cryptosystems based on algebraic coding are considered in this paper. In addition, the current state, the existing contradictions and prospects of practical use for the post-quantum period are studied. We consider estimation of resistance to attack permutation decoding and computational complexity compared to the RSA scheme. We proposed a new code cryptosystem, it significantly increases the relative information performance and keeps the main advantages of resistance to classical and quantum cryptanalysis.References
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. Handbook of Applied Cryptography – CRC Press, 1997. – 794 р.
Горбенко І.Д., Горбенко Ю.І. Прикладна криптологія. Теорія. Практика. Застосування: Підручник для вищих навчальних закладів. – Харків: Вид-во «Форт», 2013. – 880 с.
Arto Salomaa. Public-Key Cryptography, Second, Enlarged Edition. – Springer-Verlag, Berlin, Heidelberg, New York, 1996. – x+271 pp.
Nigel Smart. Cryptography: An Introduction (3rd Edition). – 432 pp. https://www.cs.umd.edu/ ~waa/414-F11/IntroToCrypto.pdf
Shor P. W. Algorithms for quantum computation: discrete logarithms and factoring // Foundations of Computer Science : Conference Publications. – 1994. – P. 124-134.
Neal Koblitz and Alfred J. Menezes. A Riddle Wrapped in an Enigma. https://eprint.iacr.org/ 2015/1018.pdf
Bernstein, Daniel J., Buchmann, Johannes, and Dahmen, Erik. Post-Quantum Cryptography. – 2009, Springer-Verlag, Berlin-Heidleberg. – 245 p.
Кузнецов А.А. Алгебраическая теория блоковых кодов и ее приложения в криптографии // Перша міжнародні наукова конференція 25–27 травня 2005р. „Теорія та методи обробки сигналів”. Тези доповідей. – К.: НАУ. – 2005. – С. 6 – 8.
McEliece R. J. A public-key cryptosystem based on algebraic coding theory. DSN Progress Report 42-44, Jet Propulsion Lab., Pasadena, CA, January-February, 1978. P. 114-116.
Сидельников В.М. Криптография и теория кодирования. Материалы конференции «Московский университет и развитие криптографии в России», МГУ. – 2002. – 22 с.
Сидельников В.М., Шестаков С.О. О системе шифрования, построенной на основе обобщенных кодов Рида-Соломона. // Дискретная математика. – 1992. – Т.4.№3. – С. 57-63.
Daniel J. Bernstein and Tanja Lange and Christiane Peters. Attacking and defending the McEliece cryptosystem. https://cr.yp.to/codes/mceliece-20080807.pdf
В. Д. Гоппа. Новый класс линейных корректирующих кодов // Пробл. передачи информ., 1970, том 6, выпуск 3, С. 24–30.
В. Д. Гоппа. На неприводимых кодах достигается пропускная способность ДСК. // Пробл. передачи информ., 1974, том 10, выпуск 1, С. 111–112.
Clark G.C., Cain J.B. Error-Correction Coding for Digital Communications. – Springer, 1981, - 432 p.
F. J. MacWilliams and N. J. A. Sloane. The theory of error-correcting codes. – North-Holland, Amsterdam, New York, Oxford, 1977, – 762 pp.
Niederreiter H. Knapsack-type cryptosystems and algebraic coding theory // Problem Control and Inform Theory, 1986, v. 15. P. 19-34.
Метод недвійкового рівновагового кодування / В. Б. Дудикевич, О. О. Кузнєцов, Б. П. Томашевський // Сучасний захист інформації. - 2010. - № 3. - С. 57-68.
Дудикевич В.Б., Кузнецов О.О., Томашевський Б.П., Максимович В.М. Спосіб формування рівновагових недвійкових послідовностей. Пат. UA 94308 U, МКІ (2006.01) H03M 7/06. – № u 2009 08173; Заявл. 03.08. 2009; Опубл. 24.04.2011, Бюл. №8, 2011р. – 4 с.
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