Yesina M. Models and methods of the electronic signatures properties comparative analysis, identification and substantiation of their use conditions

The thesis is devoted to the solution of important scientific problem, which is the development of models, methods and estimation means of the electronic signatures with appendix cryptographic stability and counteracting to attacks basic on collisions creating and key binding, the technique of their estimation and comparative analysis improving. The research object is processes of cryptographic transformations such as electronic signature (ES) with the appendix, that are used in electronic trust services, and that are based on the group of elliptic curve (EC) points operations and on the group of elliptic curve (EC) points with pairing EC points. In the thesis first the mathematical models of attack "full disclosure" realization on ES mechanisms are proposed, which are based on mathematical apparatus pairing EC points, that have polynomial complexity, and set out the proposals for possible options for their protection. Get further development: methods for estimating the security of ES mechanisms based on the identification data and anonymous signatures from potential attacks; evaluation and comparison methods of cryptographic primitives based on hierarchy analysis method and variations of the determining weight indices method, that allows to receive more accurate estimation data. The anonymous ES method on EC was improved due to the fact, that the subscriber and validator actions are the same as described in the relevant standards for the usual signature and verification in the EC points group, that allows to carry out the implementation an anonymous signature functionality into existing information and telecommunications systems so, that it does not require additional efforts, and you can also directly refer to the existing standards and not to enter into conflict with them.