Систематизація методів доказу з нульовим розголошенням

Abstract

The article systematizes modern methods of zero-knowledge proof (ZKP). Classification features are considered: protocol interactivity, algebraic or stochastic basis, need for trusted setup, type of zero-knowledge, and proof model. Classical schemes (Fiat–Shamir, Schnorr, Blum), modern zk-SNARK and zk-STARK, as well as novel approaches – PLONK, Halo 2, Bulletproofs, lattice-based ZKPs, and machine learning proofs are described. A comparative analysis is conducted according to efficiency, proof size, generation and verification complexity. It is shown that SNARKs provide compactness but require a trusted setup, while STARKs are transparent and post-quantum secure but large. Open problems are highlighted: recursive proofs, standardization, metadata protection, and applications in machine learning. It is concluded that further research in this field is aimed at creating scalable, secure, and quantum-resistant protocols for digital technologies.