In the crypto field, zero - knowledge proof, an innovative technology, has seen notable breakthroughs. For instance, in identity verification, it enables users to prove their identity without disclosing sensitive personal data, enhancing privacy. In blockchain transactions, it can verify the authenticity of transactions without revealing transaction details, improving security. Also, in decentralized finance (DeFi) applications, zero - knowledge proof helps reduce the risk of fraud by validating information privately. These real - world applications are revolutionizing the way we interact with digital assets.​