CONSTRUCTION OF AN IMPROVED ENCRYPTION SCHEME ON GENERALIZED SUZUKI 2-GROUPS IN THE MST3 CRYPTOSYSTEM

Abstract

This paper proposes a method for constructing an improved encryption scheme on generalized Suzuki 2-groups for the MST3 cryptosystem, which improves the security parameters of the original approach. The challenge of improving existing cryptosystem design approaches is driven by advances in building quantum computers with sufficient computing power to render many public-key cryptosystems insecure. In particular, this includes cryptosystems based on the factorization problem or the discrete logarithm problem, such as RSA and ECC. There have been several proposals in the past two decades for using non-commutative groups to create quantum-resistant cryptosystems. The unsolvable word problem is a promising area of research for building cryptosystems. It was formulated by Wagner and Magyarik and lies in the realm of permutation groups. Magliveras proposed logarithmic signatures, which are a special type of factorization that applies to finite groups. The latest version of this implementation, known as MST3, is based on the Suzuki group. In 2008, Magliveras demonstrated a transitive LS limit for the MST3 cryptosystem. Later, Svaba proposed the eMST3 cryptosystem with improved security parameters, achieved by adding a secret homomorphic cover. In 2018, T. van Trung proposed an MST3 approach using strong aperiodic logarithmic signatures for abelian p-groups. Kong and his colleagues conducted an extensive analysis of MST3 and noted that, since there are currently no publications on the quantum vulnerability of the algorithm, it can be considered a candidate for use in the post-quantum era. The first implementation of the cryptosystem on the generalized Suzuki 2-group does not provide encryption of the entire Suzuki 2-group and does not protect against attacks with sequential key recovery by the brute-force method. Further work has developed the idea of public cryptography using non-Abelian refinements of parameters. This paper proposes a method for constructing an encryption scheme on Suzuki 2-groups that improves the security parameters of the existing MST3 cryptosystem and solves its security problems.