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Towards advance encryption based on a Generalized Suzuki 2-groups

The article shows the method on how to improve encryption algorithm in MST3 cryptosystem for the generalized Suzuki 2 - groups. The well-known MST cryptosystem based on Suzuki groups is built on a logarithmic signature (LS) at the center of the group, resulting in a large array of logarithmic signatures. An encryption scheme based on multi-parameter noncommutative groups is proposed. The multi-parameter generalized Suzuki 2 - groups are chosen as one of the group constructions. In this case, the logarithmic signature is established for the entire group, and the secrecy of the cipher depends on the order in the group. This design allows encryption to be built that is optimized for implementation costs, which are determined by the size of the logarithmic signature and secrecy, which is dependent on the size of the keys and the final field of group representation. The main difference between the presented encryption implementation lies in the step-by-step de-encapsulation of the key from the ciphertext and associated keys using logarithmic signatures. The complexity of a key recovery attack for evaluating the secrecy of a cipher is determined by enumerating all keys using an enumeration method.