Алгоритм шифрования "QAMAL NPNS"с использованием непозиционной полиномиальной системы счисления
DOI:
https://doi.org/10.26577/JMMCS.2020.v105.i1.17Ключевые слова:
криптография, шифрование, S-блок, непозиционная полиномиальная система счисления, SP-сетьАннотация
Обработка, хранение и передача информации являются важными процессами в современном
обществе. Практическое применение криптографии стало неотъемлемой частью жизни
современного общества. В Казахстане для защиты электронной информации применяются
в основном зарубежные программные и аппаратно-программные средства. Поэтому
разработка казахстанских средств криптографической защиты безусловно является
необходимой. В данной статье описывается новый алгоритма шифрования «Qamal
NPNS», который является модификацией ранее разработанного алгоритма шифрования
«Qamal». Модификация заключается в использовании преобразования, основанного на
непозиционной полиномиальной системе счисления (НПСС). Для построения нового
алгоритма шифрования также применяется SP-сеть. Приводятся теоретическое обоснование
целесообразности применения НПСС и результаты анализа алгоритма шифрования.
Отдельно приведены результаты алгебраического криптоанализ для умножения в
непозиционных полиномиальных системах счислениях. Исследование стойкости алгоритма
для отдельных процедур показало хорошие результаты, что предполагает криптостойкость
разрабатываемого алгоритма.
Библиографические ссылки
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[23] Biyashev R. G., Nyssanbayeva S. E., "Algoritm formirovaniya elektronnoy tsifrovoy podpisi s vozmozhnost’yu obnaruzheniya i ispravleniya oshibok [Algorithm for creating a digital signature with error detection and correction]" , Cybernetics and Systems Analysis, Vol. 48, No, 4, (2012): 14-23.
[24] Biyashev R., Nyssanbayeva S., Kapalova N., Khakimov R., "Modular models of the cryptographic protection of information" , International Conference on Computer Networks and Information Security (CNIS2015), Changsha, China, (2015): 393-398.
[25] Biyashev, R.G., Kalimoldayev M.N., Nyssanbayeva, S.E., Kapalova N.A., Dyusenbayev, D.S., Algazy K.T., "Development and analysis of the encryption algorithm in nonpositional polynomial notations" , Eurasian Journal of Mathematical and Computer Applications, No. 6(2)(2018): 19-33.
[26] Biyashev R.G., Nyssanbayeva S.E., Kapalova N.A., "Sekretnyye klyuchi dlya nepozitsionnykh kriptosistem. Razrabotka, issledovaniye i primeneniye [Private keys for non-positional cryptosystems. Development, research, and application]" , LAP LAMBERT Academic Publishing, (2014): 126.
[27] Kapalova N., Dyusenbayev D., "Security analysis of an encryption scheme based on nonpositional polynomial notations" , Open Engineering, No. 6, (2016): 250-258.
242.
[2] Keith Martin, "Everyday Cryptography: Fundamental Principles and Applications" , Oxford University Press (2012): 560.
[3] Gatchenko N.A., Isaev A.S., Yakovlev A.D., "Kriptograficheskaya zashchita informatsii [Cryptographic protection of information]" , Spb: NIU ITMO (2012): 142.
[4] Camel Tanougast, "Progress in Data Encryption Research" , Nova Science Publishers Inc (2013): 158.
[5] Yaschenko V.V., "Vvedeniye v kriptografiyu [Introduction to Cryptography" , SPb: Peter (2001): 348.
[6] Douglas R. Stinson, Maura B. Paterson, "Cryptography: Theory and Practice" , Boca Raton, CRC Press, Taylor &
Francis Group (2019): 580.
[7] Tokareva N.N., "Symmetric Cryptography [Simmetrichnaya kriptografiya]" , NSU, Novosibirsk (2012): 234.
[8] Wenbo Mao, "Modern Cryptography: Theory and Practice" , Prentice Hall PTR (2003): 648.
[9] Bruce Shnier, "Applied Cryptography: Protocols, Algorithms, and Source Code in C" , John Wiley & Sons (1996): 784.
[10] William Stallings, "Cryptography and Network Security: Principles and Practice" , Pearson; 6 edition (2013): 752.
[11] F.L.Bauer, "Decrypted Secrets. Methods and maxims of cryptology" , Springer-Verlag Berlin, Fourth, Revised and Extended Edition (2006): 555.
[12] L. K. Babenko, E. A. Ischukova, "Sovremennyye algoritmy blochnogo shifrovaniya i metody ikh analiza [Modern Block Encryption Algorithms and Methods of their Analysis]" , Moscow, Helios, ARV (2006): 376.
[13] Alferov A.P., Zubov A.Yu., Kuzmin A.S., Cheremushkin A.V., "Osnovy kriptografii [Fundamentals of cryptography]" , M.: Helios ARV (2001): 479.
[14] Alferov A.P., Zubov A.Yu., Kuzmin A.S., Cheremushkin A.V., "Kontseptsiya kiberbezopasnosti "Kibershchit Kazakhstana"[Concept of Cybersecurity "Cyber Shield of Kazakhstan"]" , Approved by Decree of the Government of the Republic of Kazakhstan (2017): 407.
[15] R. G. Biyashev, S. E. Nyssanbayeva , "Algorithm for Creation a Digital Signature with Error Detection and Correction" , Cybernetics and Systems Analysis Vol. 48, No. 4, (2012): 489-497.
[16] Biyashev R., Nyssanbayeva S., Kapalova N., "The Key Exchange Algorithm on Basis of Modular Arithmetic" , Proceedings of International Conference on Electrical, Control and Automation Engineering (ECAE2013), Hong Kong ? Lancaster, U.S.A.: DEStech Publications, (2013): 16.
[17] Kapalova N., Haumen A., "The model of encryption algorithm based on non-positional polynomial notations and constructed on an SP-network" , Open Engineering, Volume 8, Issue 1, (2018): 140-146.
[18] Amerbayev V.M., Biyashev R.G., Nyssanbaeva S.E., "Use of nonpositional notations in cryptographic protection" , Izv. Nat Acad. of Sciences Resp. Kazakhstan, Ser. Phys.-Mat, No 3 (2005): 84-89.
[19] Amerbayev V.M., Biyashev R.G., Nyssanbaeva S.E., "Use of nonpositional notations in cryptographic protection" , Izv. Nat Acad. of Sciences Resp. Kazakhstan, Ser. Phys.-Mat, No 3 (2005): 84-89.
[20] Otchet o nauchno-issledovatel’skoy rabote «Razrabotka programmnykh i programmno-apparatnykh sredstv dlya kriptograficheskoy zashchity informatsii pri yeye peredache i sokhranenii v infokommunikatsionnykh sistemakh i po obshchim"[Research report "Development of software and firmware means for cryptographic protection of information during its transfer and storage in information and communications systems and general-purpose networks."], (2018), State reg. No. 0118RK01064.
[21] Kapalova N., Dyusenbayev D., "Security analysis of an encryption scheme based on nonpositional polynomial notations" , Open Engineering, No. 6, (2016): 250-258.
[22] Amerbayev V. M., Biyashev R. G., Nyssanbayeva S. E., "Primeneniye nepozitsionnykh sistem schisleniya pri kriptograficheskoy zashchite [Implementation of Non-positional Notations for Cryptographic Security]" , News of the National Academy of Science of the Republic of Kazakhstan, Physical-mathematical series, Almaty: Gylym, No. 3, (2005): 84-89.
[23] Biyashev R. G., Nyssanbayeva S. E., "Algoritm formirovaniya elektronnoy tsifrovoy podpisi s vozmozhnost’yu obnaruzheniya i ispravleniya oshibok [Algorithm for creating a digital signature with error detection and correction]" , Cybernetics and Systems Analysis, Vol. 48, No, 4, (2012): 14-23.
[24] Biyashev R., Nyssanbayeva S., Kapalova N., Khakimov R., "Modular models of the cryptographic protection of information" , International Conference on Computer Networks and Information Security (CNIS2015), Changsha, China, (2015): 393-398.
[25] Biyashev, R.G., Kalimoldayev M.N., Nyssanbayeva, S.E., Kapalova N.A., Dyusenbayev, D.S., Algazy K.T., "Development and analysis of the encryption algorithm in nonpositional polynomial notations" , Eurasian Journal of Mathematical and Computer Applications, No. 6(2)(2018): 19-33.
[26] Biyashev R.G., Nyssanbayeva S.E., Kapalova N.A., "Sekretnyye klyuchi dlya nepozitsionnykh kriptosistem. Razrabotka, issledovaniye i primeneniye [Private keys for non-positional cryptosystems. Development, research, and application]" , LAP LAMBERT Academic Publishing, (2014): 126.
[27] Kapalova N., Dyusenbayev D., "Security analysis of an encryption scheme based on nonpositional polynomial notations" , Open Engineering, No. 6, (2016): 250-258.
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Как цитировать
Biyashev, R. G., Smolarz, A., Algazy, K. T., & Khompysh, A. (2020). Алгоритм шифрования "QAMAL NPNS"с использованием непозиционной полиномиальной системы счисления. Вестник КазНУ. Серия математика, механика, информатика, 105(1), 198–207. https://doi.org/10.26577/JMMCS.2020.v105.i1.17
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