Implementation of a zero-disclosure proof algorithm in digital identity technology in the management of technological processes of the enterprise

Abstract

The paper discusses models and methods for implementing cryptographic algorithms of zero proof knowledge and discusses various forms of these algorithms, such as zk-SNARK and zk-STARK. The application of the implementation of these algorithms is discussed within the framework of building a digital (sovereign) personality system. The paper also examines in detail the zk-STARK technology, provides sequential steps and mathematical abstractions that can implement such an algorithm and apply it in the solution being designed. The implementation of the algorithm is given by the example of the formulation of the Collatz hypothesis, the construction of the query, the formation of the constraints of the query (constraints) is considered, an example of the formation of a polynomial with a high degree and the subsequent application of the FRI technology (Fast Reed-Solomon Interactive Oracle Proofs of Proximity) is described. The paper also examines the mechanism of working with the degrees of the polynomial, which allows to reduce the degree and simplify the operation of the algorithm. A new method is proposed to improve the security of systems using a distributed data registry (blockchain): the paper considers a developed prototype using zk-STARK technology, which gets rid of a trusted installation (a potential vulnerability of zk-SNARK) and implements an attack-resistant algorithm using quantum computers. The application of the algorithm is considered on the prototype of the blockchain, which allows you to issue new transactions with support for the described method. The paper presents the prototype metrics, measurement of the number of transactions per second, as well as the response time of the blockchain node and the RAM consumed by one node.