Secure formation of public parameters and elimination of vulnerabilities of zero-knowledge succint non-interactive arguments of knowledge

The methods of eliminating vulnerabilities of zero-knowledge succinct non-interactive arguments of knowlede are considered. The methods are based on the security of public parameters formation in the form of common reference strings using a trusted third party and multilateral interaction. The multilateral formation of the common reference strings uses the only honest party with a fixed and unlimited set of participants, as well as verification of the reliability of the results. Examples of increasing the level of security of zero-knowledge succinct non-interactive arguments of knowledge based on the correction of proof verification equations and the values of the common reference strings, eliminating redundant elements from the common reference strings and the keys of proof formation are given. The protocols that develop the construction of the common reference strings from static to updatable and universal versions are mentioned.