РОЗРОБКА МЕТОДИКИ ВИПРОБУВАНЬ БІБЛІОТЕКИ КРИПТОГРАФІЧНИХ ПЕРЕТВОРЮВАНЬ НА ПРИКЛАДІ КРИПТОСИСТЕМИ MST3 НА ОСНОВІ УЗАГАЛЬНЕНИХ СУЗУКІ 2-ГРУП

Abstract

The article proposes a methodology for testing a library of cryptographic transformations with the implementation of an improved encryption scheme on generalized Suzuki 2-groups in the MST3 cryptosystem. The need to improve existing methods of cryptosystem creation is driven by progress in quantum computer development, which possess sufficient computational power to compromise many existing public key cryptosystems. This is especially true for systems based on factorization and discrete logarithm, such as RSA and ECC. Over the last nearly 20 years, there have been proposals for using non-commutative groups to develop quantum-resistant cryptosystems. The unsolved word problem, formulated by Wagner and Magyarik, uses permutation groups and is a promising direction in cryptosystem development. Magliveras proposed logarithmic signatures, a special type of factorization applied to finite groups, and the latest version of this technology is known as MST3, based on the Suzuki group. The first implementation of the cryptosystem on the generalized Suzuki 2-group had limitations in encryption and protection against brute force attacks. Over the past years, many proposals have been made to improve the basic design. The research conducted by the authors expanded the possibilities of using public cryptography by refining parameters based on non-Abelian groups. The article demonstrates the methodology for conducting tests of the practical implementation of the library of cryptographic transformations with the implementation of an improved encryption scheme on Suzuki 2-groups, confirming its functionality.

Keywords: logarithmic signature, covers, MST3 cryptosystem, generalized Suzuki-2 groups, encryption scheme.