CountCrypt: Quantum Cryptography between QCMA and PP
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918154893000704 |
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| author | Goldin, Eli Morimae, Tomoyuki Mutreja, Saachi Yamakawa, Takashi |
| author_facet | Goldin, Eli Morimae, Tomoyuki Mutreja, Saachi Yamakawa, Takashi |
| contents | We construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) commitments and QCCC multiparty non-interactive key exchange exist. We also construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QMA}$, 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 $\mathbf{BQP}=\mathbf{QMA}$ but pseudorandm unitaries exist. We also show that (poly-round) 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 $\mathbf{BQP}=\mathbf{PP}$. Our results together imply that aside from pseudorandom state generators, there is a large class of quantum cryptographic primitives which can exist even if $\mathbf{BQP} = \mathbf{QCMA}$, but are broken if $\mathbf{BQP} = \mathbf{PP}$. Furthermore, one-way puzzles are a minimal primitive for this class. We denote this class ``CountCrypt''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14792 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CountCrypt: Quantum Cryptography between QCMA and PP Goldin, Eli Morimae, Tomoyuki Mutreja, Saachi Yamakawa, Takashi Quantum Physics Cryptography and Security We construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QCMA}$ but quantum-computation-classical-communication (QCCC) commitments and QCCC multiparty non-interactive key exchange exist. We also construct a unitary oracle relative to which $\mathbf{BQP}=\mathbf{QMA}$, 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 $\mathbf{BQP}=\mathbf{QMA}$ but pseudorandm unitaries exist. We also show that (poly-round) 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 $\mathbf{BQP}=\mathbf{PP}$. Our results together imply that aside from pseudorandom state generators, there is a large class of quantum cryptographic primitives which can exist even if $\mathbf{BQP} = \mathbf{QCMA}$, but are broken if $\mathbf{BQP} = \mathbf{PP}$. Furthermore, one-way puzzles are a minimal primitive for this class. We denote this class ``CountCrypt''. |
| title | CountCrypt: Quantum Cryptography between QCMA and PP |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2410.14792 |