Stern Zero-Knowledge Identification Protocol Based on Lee Distance

Post-quantum cryptography has gained urgent attention as quantum computing poses fundamental threats to traditional public-key cryptosystems. Code-based cryptography stands out as a robust post-quantum candidate, but most existing schemes are built on Hamming distance, whereas Lee distance provides a more natural error model for specific communication channels like phase-modulation channels. This paper presents the Lee–Stern zero-knowledge identification protocol, which extends the classic Stern protocol from the binary Hamming metric to the Lee metric over arbitrary prime fields. We adopt the state-of-the-art LMMT-ISD attack framework to conduct rigorous security re-evaluation and derive necessary parameter bounds for standard post-quantum security levels. Extensive experiments analyze how code length and prime modulus affect the protocol’s overheads, showing that the proposed scheme achieves equivalent security with notably shorter code length and smaller public key size than the original binary Stern protocol.