Conjugate coding based designated verifier quantum zero knowledge proof for user authentication

Zero Knowledge Proofs based on computational hardness assumptions are fundamental primitives for secure user authentication. This paper proposes a novel Designated Verifier Zero Knowledge Proof that leverages the inherent randomness of quantum bits. Unlike traditional constructions relying on computationally intractable NP problems, the proposed protocol derives its security from the physical layer, specifically the uncertainty principle of quantum state projections in misaligned measurement bases. A rigorous formal mathematical analysis establishes the completeness, soundness and zero knowledge properties of the scheme. Furthermore, the protocol’s performance is evaluated via a quantum simulator under realistic error-prone conditions. The results demonstrate that the construction is robust against dishonest parties while remaining feasible under constrained quantum resources, offering a scalable approach for secure quantum authentication.