RADIOELECTRONIC AND COMPUTER SYSTEMS

Context. Using the functions of a real variable in cryptosystems as keys allow increasing their cryptographic strength since it is more difficult to select such keys. Therefore, the development of such systems is relevant. Objective. Cryptosystems with symmetric keys are proposed for encrypting and decrypting a sequence of characters represented as a one-dimensional numerical array of ASCII codes. These keys are functions of a real variable that satisfies certain restrictions. They can be both continuous and discrete. Method. Two cryptosystem options are proposed. In the first embodiment, the transmitting and receiving sides select two functions, the first transmitted symbol, the area of the function definition, and the step of changing the function argument. Discrete messages are encrypted by calculating the first-order integral disproportion of the encrypted array using a function. The corresponding value of the second function is added to the obtained cipher of each symbol for scrambling to complicate the analysis of the intercepted message. On the receiving side, the second function is subtracted and decryption performed by the inverse transformation of the formula for integral disproportion. In the second version, sequential encryption is performed when the cipher obtained using one of the key functions in the first stage is encrypted again by calculating the disproportion using the second function, the key. Accordingly, in two stages, decryption is performed. Results. Examples of encryption and decryption of a sequence of text characters are presented. It is shown that the same character is encoded differently depending on its position in the message. In the given examples it is presented the difficulty of key functions parameters choosing and the cryptographic strength of the proposed cryptosystem. Conclusions. Variants of the cryptosystem using the first-order integral disproportion function are proposed, in which the functions of a real variable serve as keys. To “crack” such a system, it is necessary not only to select the form of each function but also to find the values of its parameters with high accuracy. The system has high cryptographic strength.

cryptosystems; disproportion functions; first-order integral disproportion function; real variable functions; key function; encryption; decryption; text messages

Shelechov, I. V., Barchenko, N. L., Kalchenko, V. V., Obodiak, V. K. A Hierarchical Fuzzy Quality Assessment of Complex Security Information Systems. Radioelectronic and computer systems, 2020, vol. 4, pp. 106-115. DOI: 10.32620/reks.2020.4.10.

Smart, N. Cryptography: An Introduction, 3rd ed., University of Bristol, 2014. 424 p. Available at: https://www.cs.umd.edu/~waa/414-F11/IntroToCrypto.pdf. (accessed 12.02.2021).

Ferguson, N., Schneier, B., Kohno, T. Cryptography Engineering: Design Principles and Practical Applications. New York, John Wiley & Sons Publ., 2010. 353 p. DOI: 10.1002/9781118722367.

Boneh, D., Shoup, V. A Graduate Course in Applied Cryptography. Version 0.5. Available at: https://toc.cryptobook.us/book.pdf. (accessed 12.02.2021).

Klyucharev, P. G. Kvantovyi komp'yuter i kriptograficheskaya stoikost' sovremennykh sistem shifrovaniya [Quantum computer and cryptographic strength of modern encryption systems]. Vestnik Moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N. E. Baumana. Seriya «Estestvennye nauki» – Bulletin of the Moscow State Technical University. N. E. Bauman. Series "Natural Sciences", 2007, no. 2, pp. 113-120.

Ladd, T. D., Jelezko, F., Laflamme, R., Nakamura, Y., Monroe, C., O’Brien, J. L. Quantum Computing. Nature, 2010, vol. 464, pp. 45-53. DOI: 10.1038/nature08812.

Grover, L. K. Quantum Mechanics Help in Searching for a Needle in a Haystack. Phys. Rev. Lett., 1997, vol. 79, pp. 325-328. DOI: 10.1103/PhysRevLett.79.325.

Shor, P. W. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM Journal on Computing, 1997, vol. 26, iss. 5, pp. 1484-1509. DOI: 10.1137/S0097539795293172.

Proos, J. A., Zalka, C. Shor’s discrete logarithm quantum algorithm for elliptic curves. University of Waterloo, 2004. 34 p. Available at: https://arxiv.org/pdf/quant-ph/0301141v2.pdf. (accessed 12.02.2021).

Kolmogorov, A. N., Fomin, S. V. Elements of the Theory of Functions and Functional Analysis Kindle Edition. 2020. 128 p. Available at: https://www.amazon.com/Elements-Theory-Functions-Functional-Analysis-ebook/dp/B08CDF9FTM. (accessed 12.02.2021).

Avramenko, V. V., Demianenko, V. M. Cryptosystem based on a key function of a real variable. CEUR Workshop Proceedings (CMIS 2020). Available at: http://ceur-ws.org/Vol-2608/paper51.pdf. (accessed 12.02.2021).

Avramenko, V. V. Kharakternye neproportsional'nosti chislovykh funktsii i ikh primenenie pri reshenii zadach diagnostiki [Characteristic disproportions of numerical functions and their application in solving diagnostic problems]. Visnyk Sums'koho derzhavnoho universytetu. Seriya : Tekhnichni nauky – Visnik of the Sumy State University. Series: Technical Sciences, 2000, vol. 16, pp. 12-20. Available at: https://essuir.sumdu.edu.ua/bitstream-download/123456789/1824/1/5201C993d01.pdf. (accessed 12.02.2021).

Carlet, Claude. Boolean Functions for Cryptography and Error Correcting Codes. Available at: https://www.math.univ-paris13.fr/~carlet/chap-fcts-Bool-corr.pdf. (accessed 12.02.2021).

Advanced encryption standard (AES) : Federal Information Processing Standards Publication 197. Effective from 2002-05-26, Gaithersburg, FIPS PUBS, 2001. 47 p. DOI: 10.6028/NIST.FIPS.197.

Hankerson, D. R. Menezes, A. J., Vanstone, S. A. Guide to elliptic curve cryptography. New York, Springer Publ., 2003. 311 p. ISBN 978-0-387-21846-5.

DSTU HOST 28147:2009 Systema obrobky informatsiyi. Zakhyst kryptohrafichnyy. Alhorytm kryptohrafichnoho peretvorennya (HOST 28147-89) [DSTU GOST 28147: 2009 Information processing system. Cryptographic protection. Cryptographic transformation algorithm (GOST 28147-89)]. Enter. 2009-02-01, Kyiv, State Standard of Ukraine, 2009. 28 p.

Rivest, R. L. Shamir, A., Adleman, L. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 1978, vol. 21, issue 2, pp. 120-126. DOI:10.1145/359340.359342.

Kessler, Gary C. An Overview of Cryptography. Available at: https://www.garykessler.net/library/crypto.html. (accessed 2.04.2021).

Bagwe, G. R., Apsingekar, D. S., Gandhare, S., Pawar, S. Voice encryption and decryption in telecommunication. 2016 International Conference on Communication and Signal Processing (ICCSP), 2016, pp. 1790-1793. DOI: 10.1109/ICCSP.2016.7754475.

Lee, B. Gi., Kim, S. C. Fundamentals of Scrambling Techniques. Scrambling Techniques for Digital Transmission. Telecommunication Networks and Computer Systems. London, Springer Publ., 1994, pp. 13-24. DOI: 10.1007/978-1-4471-3231-8_2.

Vedantam, Shanmukha Shreyas., Devaruppala, Kushalnath., Nanduri, Ravi Shankar. Enhanced Scrambled Prime Key Encryption Using Chaos Theory and Steganography. In book: Intelligent Data Communication Technologies and Internet of Things. January 2020, DOI: 10.1007/978-3-030-34080-3_12.

Karpenko, A. P. Integral'nye kharakteristiki neproportsional'nosti chislovykh funktsii i ikh primenenie v diagnostike [Integral characteristics of the disproportionality of numerical functions and their application in diagnostics]. Visnyk Sums'koho derzhavnoho universytetu. Seriya : Tekhnichni nauky – Visnik of the Sumy State University. Series: Technical Sciences, 2000, no. 16, pp. 20-25. Available at: https://essuir.sumdu.edu.ua/bitstream-download/123456789/10931/1/4_Karpenko.pdf. (accessed 12.02.2021).