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The paper proposes asymmetric cipher protocol based on matrix field over some field F . The asymmetric cipher is based on two simultaneous problems: matrix conjugator search problem (MCSP) and matrix discrete logarithm problem (MDLP). The algorithm construction does not allow performing a crypto-analysis by replacing the existing MCSP solution to the matrix decomposition problem (MDP) solution. The security parameters are defined and preliminary security analysis is presented.

Asymmetric cipher protocol using conjugacy and discrete logarithm problem