Algorithms for application of permutation operations controlled by information for implementation of cryptographic transformation of information
Abstract
The purpose and objectives of the study are to develop the ways to implement cryptographic transformation of information by synthesizing algorithms for permutation operations controlled by information, and to make the analysis of their suitability for use in cryptographic algorithms. The article provides the use of the basic group of permutation operations controlled by information based on three types of algorithms for implementing the cryptographic transformation: simple shuffling, gamma sequence with a key, gamma sequence with a key with a given number of rounds. Algorithms for application of permutation operations controlled by information for the purpose of applying them in both software and hardware means of cryptographic information protection have been developed. The effectiveness of these algorithms has been evaluated on the basis of their software implementation and statistical testing by the NIST STS test package. The analysis of statistical portraits of the received results of work of the developed algorithms for the purpose of an estimation of their suitability in the course of construction of cryptographic algorithms is carried out. It is shown that for practical implementation of cryptographic algorithm based on the use of proposed permutation operations controlled by information, it is necessary to determine the practical cryptographic stability of the algorithm, which directly depends on password length and number of operations used to encrypt information. In addition, the calculation of application algorithms variability for cryptographic transformation of several blocks of information is given. The effectiveness of using permutation operations controlled by information for cryptographic transformation is to implement the method of increasing the encryption rate, the essence of which is to use a gamma sequence as a set of commands to execute sequences of cryptographic transformation operations using these permutation operations. In the course of studying the developed algorithms for using permutation operations controlled by information for cryptographic transformation and analyzing their testing results obtained with the use of the NIST STS package, it has been determined that the most effective among the three algorithms is the algorithm based on the use of gamma with a key with a given number of rounds. Since the other two algorithms have a lower score in statistical testing, it is recommended to use them together with other cryptographic transformation algorithms in order to provide the necessary cryptographic strength
Keywords
permutation; basic operation; discrete model; cryptographic transformation; statistical testing; round; pseudo-random sequence; block diagram of the algorithm
References
[1] Ella Hassanien, and Mohamed Elhoseny, Cybersecurity and Secure Information Systems: Challenges and Solutions in Smart Environments. Springer Nature Switzerland AG, 2019.
[2] V. K. Pachghare, Cryptography and Information Security, third ed. PHI Learning Private Limited, 2019.
[3] Robert Ciesla, Encryption for Organizations and Individuals. Apress, Berkeley, CA. HELSINKI, Finland, 2020.
[4] D. J. Bernstein, "Fast-key-erasure randomnumber-generators", 2017. [Online]. Available: https://blog.cr.yp.to/ 20170723random.html.
[5] А. А. Moldovian, N. А. Moldovian, and B. Ya. Sovetov, Cryptography. St. Petersburg, Russia: Lan, 2001 [in Russian].
[6] B. Ya. Ryabko, and A. N. Fionov, Foundations of modern cryptography and steganography, 2nd ed. Moscow, Russia: Goryachaya liniya - Telekom, 2013 [in Russian].
[7] G. F. Konahovich, and A. Yu. Puzyrenko, Computer Steganography. Theory and Practice. Kiev, Ukraine: MK-Press, 2006, [in Russian].
[8] V. H. Babenko, N. V. Lada, and S. V. Lada, "Synthesis and analysis of microoperations for cryptographic transformation", in 2nd Int. Sci.-Pract. Conf. Problems of informatization. Cherkasy, 2014, pp. 9-10 [in Ukrainian].
[9] V. H. Babenko, and N. V. Lada, "Synthesis and analysis of cryptographic addition operations modulo two", Systemy obrobky informatsii, no. 2 (118), pp. 116-118, 2014 [in Ukrainian].
[10] V. H. Babenko, and N. V. Lada,, "Investigation of many cryptographic addition operations", in 2nd Int. Sci.-Pract. Conf. Information Technologies in Education, Science and Technology (ITONT-2014). Cherkasy, 2014, vol. 1, pp. 135-136 [in Ukrainian].
[11] V. H. Babenko, N. V. Lada, and S. V. Lada, "Analysis of the set of operations synth?sized on the basis of addition modulo two", in 5th Int. Sci.-Pract. Conf. Methods and means of coding, protection and consolidation of information, Vinnytsia, 2016, pp. 5457 [in Ukrainian].
[12] V. H. Babenko, N. V. Lada, and S. V. Lada, "Investigation of relationships between operations in matrix models of cryptographic transformation", Visnyk Cherkaskogo derzhavnogo tekhnologich-nogo universytetu, no. 1, pp. 5-11, 2016 [in Ukrainian].
[13] O. O. Kuznetsov, M. S. Lutsenko, A. V. Andrushkevych, O. M. Melkozerova, D. V. Novikova, and A. V. Loban, "Statistical studies of modern stream ciphers", Prikladnaya radioelektronika, no. 3, vol. 15, pp. 167-178, 2016 [in Ukrainian].
[14] V. N. Rudnitskiy, V. Ya. Milchevich, V. G. Babenko, R. P. Melnik, V. Rudnitskiy, and O. G. Melnik, Cryptographic coding: methods and means of implementation, part 2. Kharkov, Ukraine: Shchedraia usadba plius, 2014 [in Russian].
[15] Cryptographic coding: information processing and protection, V. N. Rudnytskyi, Ed. Kharkiv, Ukraine: DISA PLIUS, 2018 [in Ukrainian].
[16] T. V. Myroniuk, "Definition of elementary operations of the base group of permutations, controlled by information", Visnyk Cherkaskogo derzhavnogo tekhnologichnogo universytetu, no. 2, pp. 100-105, 2016 [in Ukrainian].
[17] J. Woodage, and D. Shumow, "An analysis of NIST SP 800-90A", in Advances in Cryptology – EUROCRYPT 2019. Lecture Notes in Computer Science, Y. Ishai and V. Rijmen, Eds., vol. 11477. Springer, Cham, 2019. [Online]. Available: https://doi.org/10.1007/978-3-030-176563_6.
[18] T. V. Myroniuk, and V. H. Babenko, "Analysis of statistical properties of cryptographic transformation results based on informationdriven permutation operations", in Int. Sci.-Pract. Conf. Innovative Current Trends in the Field of Natural Sciences, Humanities and Exact Sciences, 2017, vol. 2, pp. 41-47 [in Ukrainian].
[19] Yu. V. Shcherbyna, and S. L. Volkov, "Elements of practical implementation of frequency test of generators of cryptographic transformations", Zbirnyk naukovykh prats ODATRIA, no. 2 (3), pp. 17-21, 2013 [in Ukrainian].
[20] A. V. Potii, S. Yu. Orlova, and A. Hrynenko, "Statistical testing of random and pseudo-random number generators using the NIST STS statistical test suite". [Online]. Available: www.kievsecurity.org.ua.
[21] A. Rukhin, J. Soto, J. Nechvatal et al., "A statistical test suite for random and pseudorandom number generators for cryptographic applications". [Online]. Available: http://csrc.nist.gov/publications/nistpubs/ 800-22-rev1a/SP800-22rev1a.pdf.
[22] V. V. Bohdanov, and N. A. Palamarchuk, "Educational complex of statistical evaluation of pseudo-random and text sequences", Zbirnyk naukovykh prats Viiskovoho instytutu telekomunikatsii ta informatyzatsii Natsionalnoho tekhnichnoho universytetu Ukrainy "Kyivskyi politekhnichnyi instytut", no. 3, pp. 17-26, 2007 [in Ukrainian].