Ways to improve the performance of zero-knowledge succinct non-interactivearguments of knowledge and the analysis of the rusults achieved

We consider ways to improve the performance of zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) based on polynomial sets, such as quadratic arithmetic programs (QAP), square arithmetic programs (SAP), quadratic span programs (QSP), square span programs (SSP), quadratic polynomial programs (QPP), etc. To improve the performance of zk-SNARK, batch data processing methods, various modifications of exponentiation problems, bilinear pairings based on elliptic curves, etc. are used. A comparative analysis of the complexity of the common reference strings formation, the construction and verification of the calculations reliability proofs, as well as the sizes of common reference strings and proofs has been carried out.