Abstract Quantum commitment schemes remain challenging to deploy in practice due to the high cost and fragility of quantum communication. Although recent advances have leveraged quantum channels to improve security and efficiency, these schemes often require substantial quantum interaction, limiting their practicality. To address these challenges, we follow the emerging paradigm of quantum-computation classical-communication (QCCC) protocols, which minimize quantum communication while preserving robust security guarantees. In this work, we construct a QCCC commitment scheme that achieves statistically hiding and computationally collapse-binding-a strong binding notion previously attainable only via collapsing hash functions, which are believed to be stronger than quantum collision-resistant hash functions. In order to circumvent the obstacle of quantum rewinding for an entirely quantum adversary, our construction introduces a novel cryptographic primitive, the quantum inaccessible entropy generator (qIEG), as a quantum analogue of the classical IEG framework developed by Haitner et al. [STOC ’09]. Notably, our approach relies on potentially weaker assumptions, marking a significant step toward practically deployable and theoretically robust quantum commitments in communication-constrained quantum settings.

Abstract One-way quantum state generators (), which serve as the quantum analog of one-way functions (), have attracted significant interest due to their potential applications and the reduced assumption requirements compared to . This paper explores the applications of structured and presents several results: We construct efficiently samplable, statistically far but computationally indistinguishable pairs of distributions ( pairs) from secretly-verifiable with somewhat injectivity, which has implications for quantum commitment schemes; We demonstrate that somewhat injective can be derived from almost regular ; We also focus on a specific type of , termed , and prove that the existence of a single-copy-secure hard-core predicate for these is both necessary and sufficient for constructing pairs; Moreover, we propose a simple quantum commitment scheme based on the decisional assumption, offering improved parameter choices and flexibility over classical schemes. These findings contribute to the understanding and potential applications of in quantum cryptography.

Abstract In this paper, we further explore the properties of the verifiable random functions in both a black-box and a non-black-box manner. The results are mainly following two parts: $\bullet $ Black-Box Barrier: It is set up for an impossibility result of black-box reduction from verifiable random functions to injective one-way functions and indistinguishability obfuscators, where the verifiable random functions are suggested to be domain-invariant (i.e. the support of the distribution of keys and the domain of the evaluation space are independent of the underlying building blocks). Our result illustrates how the non-domain-invariant constructions circumvent the black-box barriers for constructing verifiable random functions and sheds light on why it is so difficult to give a domain-invariant instantiation. $\bullet $ Non-Black-Box Construction: On the other hand, the verifiable unpredictable functions are constructed from a given primitive by a non-black-box technique called the hitting-set generator. To show it's a somewhat useful technique for constructing the verifiable unpredictable functions, we further derive a limitation of the black-box barrier by proving the barrier still holds between the given primitive and verifiable unpredictable functions. Our results not only analyse the properties of verifiable random functions theoretically, but also reveal the limitation of indistinguishability obfuscators in a black-box manner, and show the advantages by adopting non-black-box techniques.