Implementation of authentication tools is the requirement for secured information system in open networks. Known authentication protocols are based on some secret knowledge (key or password) checking. Preferable scheme for checking procedure is client-server dialog without transferring of secret knowledge, even in ciphered form, also known as zero-knowledge protocol. Such protocols, as a rule, use mathematically complex problems without known simple solution for inverse calculation. This obscurity case a weakness of protocols - discovering solution of the problem impairs the secrecy of protocol. It is proposed the authentication schemes built on complex fractal sets including distant knowledge diagnostic methods. Fractal sets suitable for posed problem due to properties of finiteness and infiniteness combination. Property of finiteness allows set construction; infiniteness ensures multiple usage of the scheme. The algorithm of client-server communication is shown. Usage of authentication scheme could improve the network information resource security.

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