[Resource Topic] 2023/1279: General Non-interactive Quantum Commitments Are Compatible with Quantum Rewinding

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General Non-interactive Quantum Commitments Are Compatible with Quantum Rewinding

Authors: Jun Yan


In this work, we show that general non-interactive quantum commitments (allowing quantum computation and communication) to classical messages are compatible with current-known quantum-rewinding techniques. Specifically, we first propose a definition of collapse-binding of quantum commitments which generalizes from its post-quantum counterpart and is shown to work well with quantum rewinding. Then we show that thus defined collapse-binding is equivalent to the conceivably minimal unique-message-binding. This in particular implies that canonical quantum bit commitments are collapse-binding and can be used to instantiate many cryptographic applications.

Additionally, we rephrase the flavor conversion of canonical quantum bit commitments as a hardness conversion, which then can be used to establish a stronger quantum indistinguishability that works well with quantum rewinding just like in the post-quantum setting. Such indistinguishability allows us to establish the security of the Goldreich-Kahan construction of constant-round zero-knowledge proofs for NP instantiated with canonical quantum bit commitments. We thus for the first time construct a constant-round (actually, four-round) quantum computational zero-knowledge proof for NP based on the minimum complexity assumption that is needed for the complexity-based quantum cryptography.

ePrint: https://eprint.iacr.org/2023/1279

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