Analysis of the possibility of using modern packages of computer algebra in the synthesis of crypto-primitives: Fìz.-mat. model. ìnf. tehnol. 2021, 33:128-132 - Ponomar, Volodymyr; Onoprienko, Viktor (PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, 2021)
The paper deals with systems of computer algebra - software for symbolic calculations, which allows to conduct the entire cycle of development of a mathematical model. The paper presents the results of the analysis of systems of computer algebra with specialized purpose Magma, evaluation of the possibility of its use for modulation of processes in symmetric and asymmetric cryptographic systems, as well as recommendations for their further improvement. Magma functionality is also analyzed for evaluation of possibility to model and study promising candidates for the post-quantum standard of electronic signature algorithms, asymmetric encryption and key encapsulation, including algorithms based on cryptographic transformations in the lattice-based, the use of hash trees, mathematical codes that are undergoing research during the NIST PQC competition, as well as the draft standard "Vershina 1". References Davenport, J., Sire, I., Tournier, E. (1991). Computer algebra. M .: Mir. Bosma, W., Cannon, J. (2006). Catherine Playoust, Allan Steel. Solving Problems with Magma. School of Mathematics and Statistics. University of Sydney. Australia. Ducas, L., Kiltz, E. Tancrède Lepoint, Vadim Lyubashevsky, Peter Schwabe, Gregor Seiler and Damien Stehlé CRYSTALS-Dilithium: Algorithm Specifications and Supporting Documentation. DOI https://doi.org/10.46586/tches.v2018.i1.238-268 Gorbenko, I. D., Oleksiychuk, A. M., Kachko, O. G., Gorbenko, Yu. I., Yesina, M. V., Kandiy, S. O. (2020). Methods for calculating system parameters for electronic signature "Crystals-Dilithium" 128, 256, 384 and 512 bits of security levels. Radio engineering. - Kh .: Kharkiv National University of Radio Electronics, 202, 5-27. DOI https://doi.org/10.30837/rt.2021.1.204.02