Synthesis method of optimal substitution constructions based on the criterion of zero correlation between the output and input data vectors
DOI:
https://doi.org/10.3103/S0735272712120023Keywords:
encryption, complete code, structural properties, Hamming distance, orthogonal vectors, forms of matrix representation, periods of cycle, correlation coefficient, correlation matrix, criterion of zero correlationAbstract
Four presentation forms of canonical optimal coding sequences (OCS) that fully determine the cryptographic properties of substitution boxes (S-boxes) have been considered. In addition, the structural properties of OCS were also determined. This formed the basis for proposing a regular synthesis method of complete classes of OCS for building optimal substitution tables based on the criterion of zero correlation between the output and input data vectors.
References
B. Ya. Ryabko and A. N. Fionov, Basics of Modern Cryptography and Steganography (Goryachaya Liniya–Telekom, Moscow, 2010) [in Russian].
B. Sklar, Digital Communications: Fundamentals and Applications, 2nd ed. (Prentice-Hall, New Jersey, 2001).
V. I. Dolgov, R. V. Oleinikov, I. V. Lisitskaya, R. V. Sergienko, E. V. Drobot’ko, and E. D. Mel’nichuk, “Substitution Constructions of Modern Symmetric Block Ciphers,” Radioelektronni i Kompyuterni Systemy, No. 6, 89 (2009).
M. I. Mazurkov, V. Ya. Chechelnytskyi, and K. K. Nekrasov, “Three-Level Cryptographic System for Block Data Encryption,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 50 (7), 43 (2007) [Radioelectron. Commun. Syst. 50 (7), 376 (2007)], DOI: 10.3103/S0735272710070058.
V. P. Ipatov, Broadband Systems and Code Division of Signals. Principles and Applications (Tekhnosfera, Moscow, 2007) [in Russian].
M. I. Mazurkov, Broadband Wireless Systems: Tutorial for Higher School Students (Nauka i Tekhnika, Odessa, 2010) [in Russian].
