MicroCrypt Assumptions with Quantum Input Sampling and Pseudodeterminism: Constructions and Separations
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| author | Barhoush, Mohammed Nishimaki, Ryo Yamakawa, Takashi |
| author_facet | Barhoush, Mohammed Nishimaki, Ryo Yamakawa, Takashi |
| contents | We investigate two natural relaxations of quantum cryptographic primitives. The first involves quantum input sampling, where inputs are generated by a quantum algorithm rather than sampled uniformly at random. Applying this to pseudorandom generators ($\textsf{PRG}$s) and pseudorandom states ($\textsf{PRS}$s), leads to the notions denoted as $\textsf{PRG}^{qs}$ and $\textsf{PRS}^{qs}$, respectively. The second relaxation, $\bot$-pseudodeterminism, relaxes the determinism requirement by allowing the output to be a special symbol $\bot$ on an inverse-polynomial fraction of inputs.
We demonstrate an equivalence between bounded-query logarithmic-size $\textsf{PRS}^{qs}$, logarithmic-size $\textsf{PRS}^{qs}$, and $\textsf{PRG}^{qs}$. Moreover, we establish that $\textsf{PRG}^{qs}$ can be constructed from $\bot$-$\textsf{PRG}$s, which in turn were built from logarithmic-size $\textsf{PRS}$. Interestingly, these relations remain unknown in the uniform key setting.
To further justify these relaxed models, we present black-box separations. Our results suggest that $\bot$-pseudodeterministic primitives may be weaker than their deterministic counterparts, and that primitives based on quantum input sampling may be inherently weaker than those using uniform sampling.
Together, these results provide numerous new insights into the structure and hierarchy of primitives within MicroCrypt. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | MicroCrypt Assumptions with Quantum Input Sampling and Pseudodeterminism: Constructions and Separations Barhoush, Mohammed Nishimaki, Ryo Yamakawa, Takashi Quantum Physics Cryptography and Security We investigate two natural relaxations of quantum cryptographic primitives. The first involves quantum input sampling, where inputs are generated by a quantum algorithm rather than sampled uniformly at random. Applying this to pseudorandom generators ($\textsf{PRG}$s) and pseudorandom states ($\textsf{PRS}$s), leads to the notions denoted as $\textsf{PRG}^{qs}$ and $\textsf{PRS}^{qs}$, respectively. The second relaxation, $\bot$-pseudodeterminism, relaxes the determinism requirement by allowing the output to be a special symbol $\bot$ on an inverse-polynomial fraction of inputs. We demonstrate an equivalence between bounded-query logarithmic-size $\textsf{PRS}^{qs}$, logarithmic-size $\textsf{PRS}^{qs}$, and $\textsf{PRG}^{qs}$. Moreover, we establish that $\textsf{PRG}^{qs}$ can be constructed from $\bot$-$\textsf{PRG}$s, which in turn were built from logarithmic-size $\textsf{PRS}$. Interestingly, these relations remain unknown in the uniform key setting. To further justify these relaxed models, we present black-box separations. Our results suggest that $\bot$-pseudodeterministic primitives may be weaker than their deterministic counterparts, and that primitives based on quantum input sampling may be inherently weaker than those using uniform sampling. Together, these results provide numerous new insights into the structure and hierarchy of primitives within MicroCrypt. |
| title | MicroCrypt Assumptions with Quantum Input Sampling and Pseudodeterminism: Constructions and Separations |
| topic | Quantum Physics Cryptography and Security |
| url | https://arxiv.org/abs/2505.14461 |