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

Abstract

This article presents a new encryption method based on the group of automorphisms of Suzuki's functional field, which enhances the security level of the existing MST3 cryptosystem. This approach is a response to the progress in developing powerful quantum computers, which can threaten the security of many public-key encryption systems, particularly those based on factorization and discrete logarithm problems, such as RSA or ECC. Using non-commutative groups to create quantum-resistant cryptosystems has been a known approach over the last two decades. The unsolvable word problem, proposed by Wagner and Magyarik, applied in the realm of permutation groups, 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 implementation, known as MST3, is based on the Suzuki group. In 2008, Magliveras presented the LS limit of transitivity for the MST3 cryptosystem. Later, Svaba proposed an improved version of the cryptosystem eMST3 with enhanced protective features, including secret homomorphic covering. In 2018, T. van Trung suggested the application of the MST3 approach using strong aperiodic logarithmic signatures for Abelian p-groups. Kong and his colleagues conducted an in-depth analysis of MST3 and noted that due to the lack of publications on the quantum vulnerability of this algorithm, it can be considered as a potential candidate for use in the post-quantum era. One of the key ideas is to increase encryption efficiency by optimizing computational resources, particularly through reducing the size of the key space. This method is applied to the calculations of logarithmic signatures within the group. It was implemented over finite fields of small sizes.