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This thesis deals with multivariate cryptography. It includes specifically a description of the MQ problem and the proof of it's NP-completness. In the part of the MQ problem there is a description of a general pattern for the creation of the public part of asymetric cryptosystems based on the MQ problem. It this part the thesis describes the QMLE problem, which is important for the figure of the cryptosystem private key based on the MQ problem. Further, the thesis includes a description of the influence of the structure display, which appears in the QMLE problem, on time solution complexity of QMLE problem. The influence of time complexity has been detected by means of experimental measurement with programed algorithm. At the end of the thesis there is specified description of selected multivariety cryptosystems based on the MQ problem. Selected cryptosystems are provided with detailed description of encryption and decryption by means of selected cryptosystems and time estimations of these operations. The thesis includes estimations of memory requirements on saving of private and public key of the selected cryptosystems. Powered by TCPDF (www.tcpdf.org)