New asymmetric cipher based on matrix power function is presented. Cipher belongs to the class of recently intensively evolving non-commuting cryptography due to expectation of its resistance to potential quantum cryptanalysis.

The algebraic structures for proposed cipher construction are defined. Security analysis was performed and security parameters are defined. On the base of this research the secure parameters values are determined. The comparison of efficiency of microprocessor realization of proposed algorithm with different security parameters values is presented.