Abstract
AbstractThis article describes a new implementation of MST-based encryption for generalized Suzuki 2-groups. The well-known MST cryptosystem based on Suzuki groups is built on a logarithmic signature at the center of the group, resulting in a large array of logarithmic signatures. An encryption scheme based on multiparameter non-commutative groups is proposed. The multiparameter generalized 2 - Suzuki group was chosen as one of the group constructions. In this case, a logarithmic signature is established for the entire group. The main difference from the known one is the use of homomorphic encryption to construct coverings of logarithmic signatures for all group parameters. This design improves a secrecy of the cryptosystem is ensured at the level of a brute-force attack.
Highlights
IntroductionRecent advances in quantum computing for solving complex problems formulate new trends for building secure public-key cryptosystems
In 2009, Lempken et al described an MST3 public-key cryptosystem based on a logarithmic signature and a Suzuki 2-group [2]
In 2018, T. van Trung [7] proposed a general method for constructing strong aperiodic logarithmic signatures for Abelian p-groups, which is a further contribution to the practical application of MST cryptosystems
Summary
Recent advances in quantum computing for solving complex problems formulate new trends for building secure public-key cryptosystems. The word complexity problem was proposed by Wagner and Magyarik [1] and implemented in several cryptosystems. One of the best known and most studied is a cryptosystem based on factorization in finite groups of permutations, called the logarithmic signature [2]. In 2009, Lempken et al described an MST3 public-key cryptosystem based on a logarithmic signature and a Suzuki 2-group [2]. In 2010, Swaba et al [5] analyzed all known attacks on MST cryptography and built a more secure eMST3 cryptosystem by adding a secret homomorphic coverage. The construction of MST cryptosystems based on multiparameter non-commutative groups was proposed in [7–9]. The first implementation of the cryptosystem on the generalized Suzuki 2-group is presented in [8] and does not provide protection against brute force attacks with sequential brute force key recovery. A secure encryption scheme is proposed based on the generic Suzuki 2-group with homomorphic encryption
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