CRYPTOGRAPHIC PROTOCOL ZERO-KNOWLEDGE PROOF ON ELLIPTIC CURVES USING ONE-WAY HASH-FUNCTION

Abstract

Proposed cryptographic protocol with zero-knowledge proof on elliptic curves using one-way hash function, allowing to establish the truth of allegation and does not convey any additional information about the approval. Cryptographic protocols based on zero-knowledge proof allow identification, key exchange and other cryptographic operations to be performed without leakage of sensitive information during the information exchange. The implementation of the cryptographic protocol of the zero-knowledge proof on the basis of the mathematical apparatus of elliptic curves allows to significantly reduce the size of the protocol parameters and increase the cryptographic stability (computational complexity of the hacking problem). The security of cryptosystems on elliptic curves is based on the difficulty of solving the elliptic curve discrete logarithm problem. The completeness and correctness of the protocol is determined in the work, an example of calculation is given, the cryptographic protocol is modeled on the High-Level Protocol Specification Language, the model validation and verification of the protocol are performed. Software verification of the cryptographic protocol was performed using the software modules On the Fly Model Checker and Constraint Logic based Attack Searcher. To validation the cryptographic protocol for resistance to intruder attacks was used the Security Protocol Animator package for Automated Validation of Internet Security Protocols and Applications. The security of the proposed cryptographic protocol is based on the difficulty of solving the elliptic curve discrete logarithm problem and the cryptographic stability of the hash function. To implement the cryptographic protocol, you can use the recommended elliptical curves according to DSTU 4145-2000 and the hash function GOST 34.311-95.