Zero-knowledge proof authentication protocols

The paper presented the comparative analysis of the authentication Shnorr's protocol and the authentication protocol based on the task of finding a Hamilton cycle in the graph. It is shown that with the use of CUDA technology the productivity of protocols on graphs is as high as Shnorr's protocol productivity. The importance of such research is that protocols on graphs (the authentication protocol on the basis of the proof of graph isomorphism, the authentication protocol based on the task of finding a Hamilton cycle in the graph, etc.) have the property of zero-knowledge proof. These protocols are based on $NP$ complete tasks therefore they are independent of quantum computings, namely, are resistant to the quantum attacks. Also the modified algorithms of two-step authentication protocols with zero-knowledge proof based on asymmetric ciphers with the use of elliptic curves are also given.