New Complex Sinusoidal Waveform-Based Zero-Knowledge Proof Systems for Efficient Anonymous Authentication

Zero-knowledge proof systems based on Feige-Fiat-Shamir (FFS) protocol are an interactive protocol between two anonymous authentication parties. However, they require heavy computations because of many iterations for reducing the probability that an attacker can trick a remote server. The algorithm's time complexity rapidly increases with the total number of the challenge values, which should be unpredictable. Hence, the FFS protocol is not suitable for practical zero-knowledge proof systems. In this study, we propose new zero-knowledge proof systems based on phase mask generation that are complex sinusoidal waveform versions of the FFS algorithm for efficient anonymous authentication in the diverse interactive systems. The proposed anonymous authentication schemes need a single iteration only, allowing for efficient uses of a random challenge mask with large bit-depth. The proposed schemes allow the verifier to verify that the prover knows the secret mask, such as binary pattern, visual image, or hologram, which are the prover's secrets, without revealing any information about it to anyone else, including the verifier. Various numerical simulations demonstrate the proposed schemes' feasibility and robustness.