Abstract
The work suggests a new approach to the formation of the functions used in cryptography and cryptanalysis with use of alternative forms of Boolean functions representation. Alternative forms of Boolean functions representation is forms which differ from the classical form, which formed in the boolean basis AND-OR-NOT. As an example, is con-sider the procedure of formation of cryptographic functions with the use of alternative forms of representation, namely Cognate-forms of Boolean functions representations. This form inherently is multivariate and allows you to choose the best option from a set of possible and permissible. Moreover admissibility criteria can also be selected depending on the particular situation, since it is known that an improvement in one criterion usually leads to a deterioration of the others. In this case, using Cognate-form, we can select the necessary solution of many possible. It is shown that the use of this forms of representation of Boolean functions in the construction of cryptographic functions, algorithms and devices can be significantly improve their parameters and properties. And when they are used in cryptographic means of protection to optimize the process of logical design of cryptographic devices and improve the security of information and commu-nication systems
Keywords: cryptography, cryptographic functions, cryptographic properties, forming algorithms cryptographic functions, Cognate-forms of Boolean functions representations, alternative forms of representation of Boolean functions, Cognate implementation, information security
References
[1] Kochkarev Yu., Kazarinova N., Panteleeva N., Shakun S. Katalog-spravochnik «Klassicheskie i al'ternativnye mini-mal'nye formy logicheskikh funktsii». Monografiia [Catalog-Directory «Classic and alternative minimum form of logical func-tions.» Monograph], Cherkasy, 1999, 195 p. [2] Kochkarev Yu., Osipenkova I., Panasko E. Ortogonal forms of presentation of boolean functions in device blocks. Vestnik Cherkasskogo gosudarstvennogo tekhnologicheskogo universiteta – Bulletin of Cherkasy state technological univer-sity, 2009, pp. 39–42. [3] Kochkarev Yu., Kushch S., Predstavlenie i realizatsiia logicheskikh funktsii v rodstvennoi forme [Justification of a Cognate-form of representation and realization of logical functions]. 2010. Elektronnoe modelirovanie – Electronic Modeling, v. 33(6), pp. 73–80. [4] Kochkarev Yu., Kushch S. Rodstvennaia realizatsiia logicheskikh funktsii na osnove ikh predstavleniia v izomorfnoi forme [A Cognate-realization of logic functions on the basis of their representation in isomorphic form], 2012, Elektronnoe modelirovanie – Electronic Modeling, v. 34(4), pp. 119–123. [5] Kochkarev Yu., Kushch S., Tekhnologiia Cognate-realizatsii logicheskikh funktsii [Technology of Cognate-implementation of logic functions], 2011, Vestnik Cherkasskogo gosudarstvennogo tekhnologicheskogo universiteta – Bulletin of Cherkasy state technological university, 3, pp. 35–38. [6] Veroiatnostnaia model' formirovaniia nelineinykh uzlov zamen dlia simmetrichnykh kriptograficheskikh sredstv zashchity informatsii [Probabilistic model of substitution box generation for symmetric cryptographic methods of information security], L.S. Soroka, A.A. Kuznetsov, I.V. Moskovchenko, S.A. Isaev. Sistemy obrabotki informatsii – Information process-ing system, CUPS, 2009, v. 3 (77), pp. 101–104. [7] Tokareva N.N. Bent functions with stronger nonlinear properties: K-bent functions. Journal of Applied and Indus-trial Mathematics, vol. 2, issue 4, pp. 566–584. DOI: 10.1134/S1990478908040133. [8] Courtois N., Meier W. Algebraic attacks on stream ciphers with linear feedback. Lecture Notes in Computer Sci-ence, 2003, vol. 2656, pp. 345–359. DOI: 10.1007/3-540-39200-9_21. [9] Evertse J.H. Linear Structures in Block Ciphers. Proceedings of Eurocrypt'87, 1987, pp. 249–266. [10] Siegenthaler T. Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Trans. on Inform. Theory, 1984, vol. 5, pp. 776–780.
