Method of encryption in the MST3 cryptosystem based on Automorphisms group of Suzuki's functional field

Abstract

This article presents a new implementation of encryption based on MST, focused on generalized Suzuki 2-groups. The well-known MST cryptosystem, based on Suzuki groups, is constructed using a logarithmic signature at the center of the group, leading to a large array of logarithmic signatures. The proposed encryption is based on multi-parameter noncommutative groups, with a focus on the generalized multi-parameter Suzuki 2-group. This approach responds to the progress in the development of quantum computers, which may pose a threat to the security of many open cryptosystems, especially those based on factorization problems and discrete logarithms, such as RSA or ECC. The use of noncommutative groups to create quantum-resistant cryptosystems has been a known approach for the last two decades.
 The unsolvable word problem, proposed by Wagner and Magyarik, is used in the field of permutation groups and is key to the development of cryptosystems. Logarithmic signatures, introduced by Magliveras, represent a unique type of factorization suitable for finite groups. The latest version of such an implementation, known as MST3, is based on the Suzuki group. In 2008, Magliveras introduced the LS transitivity limit for the MST3 cryptosystem, and later Swaba proposed an improved version of the cryptosystem, eMST3. In 2018, T. van Trung suggested applying the MST3 approach using strong aperiodic logarithmic signatures for abelian p-groups. Kong and his colleagues conducted a deep analysis of MST3 and noted that due to the absence of publications on the quantum vulnerability of this algorithm, it can be considered a potential candidate for use in the post-quantum era.
 The main distinction of the new system is the use of homomorphic encryption to construct logarithmic signature coverings for all group parameters, which improves the secrecy of the cryptosystem, particularly against brute-force attacks.