In this paper I examine the possibilities of subject authentification, cryptographic methods of authentification in symmetrical and asymmetrical criptology systems (for instance, on-line and off-line regimes authentification; authentification with the participation of a two servers or an arbiter, etc.). Much attention was given to study, analyzing possibilities of computer trespasser to penetrate into the protocol, to deceive the authentification server, to change public key by its own public key, etc. A more detailed study of three protocols was carried out (Feige-Fiat-Shamir, GQ and Schnorr), concrete examples of these protocols are described, and made conclusions about safety of protocols, probability of forgery, on selection of more suitable parameters.