One of important issues of information security in the interaction of users is the use of methods and tools, allowing one party to make sure of the authenticity of another party. The proof of knowledge protocols which have the additional property of zero-knowledge are applied to solve this problem. The protocols based on asymmetric encryption have received wide acceptance, such as the Fiat-Shamir, Schnorr, Okamoto, Guillou-Quisquater, Brickell-McCurley, Feige-Fiat-Shamir protocols. Cryptographic strength of these protocols is defined by discrete logarithms in a finite prime field, as well as an increase in the number of accreditation cycles. As a result of the development of methods and tools of cryptanalysis and rapid development of technologies and power of computing systems, there is a need to increase the sizes of system-wide parameters of the protocol, leading to increased resource intensity and performance complexity of basic operations in the fields.Cryptographic zero-knowledge protocols on elliptic curves are proposed in the paper. The strength of cryptosystems on elliptic curves is based on the difficulty of solving the discrete logarithm problem in the group of elliptic curve points, and is more difficult than the discrete logarithm problem in the finite field. The completeness and soundness of protocols were determined, computation examples were given. The tools of the Strength Protocol Animator package were applied to verify the protocols for resistance to enemy attacks. Consequently, the use of cryptographic protocols on elliptic curves will significantly reduce the sizes of protocol parameters and increase the cryptographic strength

Предложены криптографические протоколы доказательства с нулевым разглашением знания на эллиптических кривых, позволяющие установить истинность утверждения и при этом не передавать какой-либо дополнительной информации о самом утверждении, а также значительно уменьшить размеры параметров протокола и увеличить криптографическую стойкость.

Запропоновані криптографічні протоколи доказу із нульовим розголошенням знання на еліптичних кривих, що дозволяють встановити істинність твердження й при цьому не передавати якої-небудь додаткової інформації про саме твердження, а також значно зменшити розміри параметрів протоколу й збільшити криптографічну стійкість.