Structure peculiarities of the finite vector groups and their use in the cryptoscheme design

Its is shown that problem of finding discrete logarithm to the multi-dimension base is an attractive primitive for designing fast signature schemes using computations in the finite vector groups. Other introduced primitive called problem of finding discrete logarithm in a hidden cyclic subgroup of the finite non-commutative group represents interest for designing fast public key agreement protocols and commutative encryption algorithms. For implementing such cryptoschemes finite non-commutative groups of four dimension vectors are proposed.