On the Security of a Realization of Cryptosystem Mst3

A new type of public key cryptosystem, called MST3, has been recently developed on the basis of logarithmic signatures and covers of finite groups. The Suzuki 2-groups have been suggested for a possible realization of the generic version of MST3. On one hand, due to their structure, the Suzuki 2-groups allow one to study the security complexity of the system, on the other hand they possess a simple presentation allowing for an efficient implementation of the system. In this paper we present a detailed study of the security of this realization of MST3. We prove a new general bound for the security complexity of MST3. This bound has size q = 2, where q is the order of the underlying finite field Fq, on which the Suzuki 2-group A(m, θ) is defined. Further, by exploiting properties of the group operation in the Suzuki 2-groups, as well as a special property of canonical transversal logarithmic signatures for elementary abelian 2-groups, we show that canonical transversal logarithmic signatures are unfit to use in this realization of MST3.