Construction of a three-parameter encryption scheme on Hermitian groups in the MST3 cryptosystem

Abstract

The article proposes a method for constructing a three-parameter encryption scheme based on Hermitian groups, which improves the security parameters of the existing MST3 cryptosystem. The challenge of improving existing approaches to building cryptosystems is driven by successes in building a quantum computer with sufficient computing power to render many public-key cryptosystems insecure. In particular, we are talking about those cryptosystems based on the complexity of factorization or the discrete logarithm problem, such as RSA, ECC, etc. There are several proposals that have become classic over the past almost 20 years for using non-commutative groups to build quantum-resistant cryptosystems The unsolvable word problem is an interesting area of research for cryptosystem construction. It was formulated by Wagner and Magyarik and lies in the plane of application of permutation groups. Logarithmic signatures (LS) were proposed by Magliveras. In this context, the logarithmic signature is a special type of factorization, it is applied to finite groups. The latest version of this implementation is known as MST3 and is based on the Suzuki group.
 In 2008, Magliveras demonstrated a transitive limit of LS for the MST3 cryptosystem. Svaba later proposed the eMST3 cryptosystem with improved security options. A secret homomorphic cover was added for this improvement. Then, in 2018, T. van Trung proposed an MST3 approach using strong aperiodic LS for abelian p-groups. Kong and colleagues conducted an extensive analysis of MST3 and noted that since there are no publications yet on the quantum vulnerability of the algorithm, it can be considered a candidate for the post-quantum era.
 One valuable idea is to improve encryption efficiency by optimizing the computational overhead. This is done while reducing the large size of the key space. This approach can be applied to LS calculations outside the center of the group. And this was done over the final fields of the small dimensions using groups with high order.