Oracle Separation Between Quantum Commitments and Quantum One-wayness
John Bostanci, Boyang Chen, Barak Nehoran
TL;DR
The paper proves a strong oracle separation between quantum commitments and quantum one-wayness by constructing a unitary oracle where commitments exist but efficient one-way state generators do not. It introduces both a polynomial-space threshold-search attack to rule out OWSG relative to common reference states and a CHRS-based construction of one-way puzzles, enabling EFI/commitments to exist while OWSG fails, thereby ruling out black-box reductions. The work also discusses a conceptual Entanglementia world and shows that several related primitives maintain their minimal status under these oracle separations, with concurrent work reinforcing the separations in related models. Overall, the results position quantum commitments (and EFI-like primitives) as strictly weaker, in a black-box sense, than most other known quantum cryptographic primitives and motivate a refined hierarchy for quantum cryptography.
Abstract
We show that there exists an oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Both have been widely considered candidates for replacing one-way functions as the minimal assumption for cryptography: the weakest cryptographic assumption implied by all of computational cryptography. Recent work has shown that commitments can be constructed from one-way state generators, but the other direction has remained open. Our results rule out any black-box construction, and thus settles this crucial open problem, suggesting that quantum commitments (as well as its equivalency class of EFI pairs, quantum oblivious transfer, and secure quantum multiparty computation) appear to be strictly weakest among all known cryptographic primitives.