An analysis of some key distribution public systems based on non-abelian groups

We consider some cryptosystems for public distribution of keys based on the composition of the conjugacy and discrete logarithm problems for non-abelian (non-commutative) groups constructed on $(\mathbf Z_p)^4$. It is proved that for these schemes the upper bound of complexity of breaking the secret key does not exceed (in the order) the complexity of discrete logarithm problem for cyclic subgroup of the multiplicative group of the field $(\mathbf Z_p)$ or its quadratic extension.