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Post-quantum ZKP protocol based on LWE and non-unitary quantum operations

This paper presents a novel hybrid zero-knowledge proof protocol resistant to quantum computer attacks. The protocol combines classical cryptography based on the Learning with Errors problem complexity with quantum state properties. The main objective of the protocol is to enable a prover to convince a verifier of knowledge of a secret parameter alpha without revealing its value, even against adversaries with quantum computational capabilities. A key feature of the protocol is the explicit dependence of quantum operations on the secret parameter through a cryptographic hash function modeled as a quantum random oracle. This ensures an inseparable connection between the quantum and classical phases of protocol execution. The protocol includes a mechanism for regular secret updates between interaction rounds, providing protection against adaptive attacks. Special attention is given to accounting for real physical errors of quantum devices – a difference threshold is introduced that allows for a certain level of noise and decoherence. The paper presents a formal security analysis of the protocol. The properties of honest-verifier zero-knowledge and proof of knowledge against quantum polynomial-time adversaries are proven. Security is justified through constructing a sequence of hybrid games showing that the probability of a successful attack is negligible relative to the security parameter plus the probability of physical implementation error. The protocol is of practical interest for building cryptographic systems in the context of quantum computing development. Read more...