This article describes the General principle of operation (stages, parameters used) of the ZK-SNARK zero-knowledge proof scheme, the possibility and prospects for its improvement. Implementations of zk-SNARK that are currently known have scalability limitations that depend on the magnitude of the computation being proved. First, the size of the proving key depends at least linearly on the upper bound of the structure in which we work. Second, the proof requires a record of all previous steps. The article describes an algorithm for achieving a new implementation of zk-SNARK using elliptic curve cryptography, field structure features, and proof integrity. In practice, this implementation is a recursive composition of the proof, while generating keys for any size of calculations carries constant memory costs. Subsequently, the entire process of proof is solely multiplicative constant costs overtime and additivecosts in memory. Thus, the described implementation of zk-SNARK has two important properties: capacity and incremental computability.