Zero-knowledge succinct non-interactive arguments of knowledge based on sets of polynomials

The paper discusses the basic principles of construction and main types zeroknowledge succinct non-interactive argument knowledge (zk-SNARK) which is used in model a three-way insecure computing environment based on sets polynomials. A number zk-SNARK cryptographic protocols with different algorithms for generating public parameters (Trusted Setup) are given, constructing proofs reliability calculations (Prover) public/designated verification (Verifier). cases satisfying feasibility discrete functions (arithmetic/ Boolean circuits) using polynomial presented quadratic arithmetic programs (QAP), square (SAP), span (QSP), (SSP), (QPP), etc., also use authenticated data described. transformations needed to build zk-SNARKs symmetric asymmetric hash functions, exponential problems, digital signatures, homomorphic encryption, bilinear pairings elliptic curves, etc. presented. Examples multilateral verifiable given.