CountCrypt: Quantum Cryptography between QCMA and PP

• URL: http://arxiv.org/abs/2410.14792v2
• Date: Thu, 24 Oct 2024 14:23:39 GMT
• Title: CountCrypt: Quantum Cryptography between QCMA and PP
• Authors: Eli Goldin, Tomoyuki Morimae, Saachi Mutreja, Takashi Yamakawa,
• Abstract summary: We construct a quantum oracle relative to which BQP = QCMA but quantum-computation-classical-communication key exchange, QCCC commitments, and two-round quantum key distribution exist. We also show that QCCC key exchange, QCCC commitments, and two-round quantum key distribution can all be used to build one-way puzzles.
• Score: 7.408475650692233
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• Abstract: We construct a quantum oracle relative to which BQP = QCMA but quantum-computation-classical-communication (QCCC) key exchange, QCCC commitments, and two-round quantum key distribution exist. We also construct an oracle relative to which BQP = QMA, but quantum lightning (a stronger variant of quantum money) exists. This extends previous work by Kretschmer [Kretschmer, TQC22], which showed that there is a quantum oracle relative to which BQP = QMA but pseudorandom state generators (a quantum variant of pseudorandom generators) exist. We also show that QCCC key exchange, QCCC commitments, and two-round quantum key distribution can all be used to build one-way puzzles. One-way puzzles are a version of "quantum samplable" one-wayness and are an intermediate primitive between pseudorandom state generators and EFI pairs, the minimal quantum primitive. In particular, one-way puzzles cannot exist if BQP = PP. Our results together imply that aside from pseudorandom state generators, there is a large class of quantum cryptographic primitives which can exist even if BQP = QCMA, but are broken if BQP = PP. Furthermore, one-way puzzles are a minimal primitive for this class. We denote this class "CountCrypt".

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