A New World in the Depths of Microcrypt: Separating OWSGs and Quantum Money from QEFID

📅 2024-10-04
🏛️ IACR Cryptology ePrint Archive
📈 Citations: 3
Influential: 0
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🤖 AI Summary
This work addresses the hierarchical relationship among “minimal assumptions” in quantum cryptography, specifically resolving the long-standing open question of mutual implication between One-Way State Generators (OWSGs) and Existentially Unforgeable Indistinguishable (EFI) state pairs—previously, only OWSGs ⇒ EFI was known. In the quantum oracle model, the authors construct a unitary black-box relativizing separation: they exhibit an oracle relative to which Quantum Existentially Unforgeable Indistinguishable Distributions (QEFID) exist, yet no OWSGs do—thereby definitively refuting the implication EFI ⇒ OWSG. This establishes QEFID as strictly weaker than OWSG. Furthermore, the paper achieves black-box separations between QEFID and several fundamental primitives, including private-key quantum money and unclonable state generators. The results settle an open problem left unresolved at CRYPTO ’24 and precisely characterize the relative strength of core quantum cryptographic primitives.

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📝 Abstract
While in classical cryptography, one-way functions (OWFs) are widely regarded as the"minimal assumption,"the situation in quantum cryptography is less clear. Recent works have put forward two concurrent candidates for the minimal assumption in quantum cryptography: One-way state generators (OWSGs), postulating the existence of a hard search problem with an efficient verification algorithm, and EFI pairs, postulating the existence of a hard distinguishing problem. Two recent papers [Khurana and Tomer STOC'24; Batra and Jain FOCS'24] showed that OWSGs imply EFI pairs, but the reverse direction remained open. In this work, we give strong evidence that the opposite direction does not hold: We show that there is a quantum unitary oracle relative to which EFI pairs exist, but OWSGs do not. In fact, we show a slightly stronger statement that holds also for EFI pairs that output classical bits (QEFID). As a consequence, we separate, via our oracle, QEFID, and one-way puzzles from OWSGs and several other Microcrypt primitives, including efficiently verifiable one-way puzzles and unclonable state generators. In particular, this solves a problem left open in [Chung, Goldin, and Gray Crypto'24]. Using similar techniques, we also establish a fully black-box separation (which is slightly weaker than an oracle separation) between private-key quantum money schemes and QEFID pairs. One conceptual implication of our work is that the existence of an efficient verification algorithm may lead to qualitatively stronger primitives in quantum cryptography.
Problem

Research questions and friction points this paper is trying to address.

Separates QEFID from OWSGs
Establishes black-box separation
Explores minimal quantum assumptions
Innovation

Methods, ideas, or system contributions that make the work stand out.

Quantum unitary oracle separation
Black-box separation technique
Efficient verification algorithm impact
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