Efficient non-interactive zero-knowledge proofs for quantum range verification in blockchain

Blockchain technology is incredibly popular nowadays which is based on a distrusted ledger technology (DLT) and decentralized database that stores encrypted blocks of data in transparency to the public. In this paper, we proposed a Quantum Range Proof a new non-interactive zero-knowledge (NIZK) proof protocol containing logarithmically small proof that lacks a trusted system. A NIZK argument is provided for the satisfy ability of a quantum circuit containing quantum range proof complexities that logarithmically grow in the quantum circuit size. The witness complexities a referred to as probability distribution measurement and for a quantum circuit containing N-dimensional complex space \((\alpha , \beta )\) $(\alpha ,\beta )$ , the soundness property of our argument convinces a verifier with the probability of quantum range proof. A novel argument system is an effective non-interactive zero knowledge of opening witness that lies between inner product spaces over the spin in N-dimension complex space. The inner product space requires logarithmic time complexity to find the witness in quantum range proof for both verifier and prover. In addition to this, a commitment schema is developed to attain a non-polynomial probability distribution and the witness at an arbitrary point in quantum state in a demonstrable manner is revealed. The efficiency of quantum range proof is particularly well suited for the non-polynomial probability distribution and trustless nature of blockchain.