From Worst-Case Hardness of $\mathsf{NP}$ to Quantum Cryptography via Quantum Indistinguishability Obfuscation

• URL: http://arxiv.org/abs/2506.19542v1
• Date: Tue, 24 Jun 2025 11:50:33 GMT
• Title: From Worst-Case Hardness of $\mathsf{NP}$ to Quantum Cryptography via Quantum Indistinguishability Obfuscation
• Authors: Tomoyuki Morimae, Yuki Shirakawa, Takashi Yamakawa,
• Abstract summary: Indistinguishability obfuscation (iO) has emerged as a powerful cryptographic primitive with many implications.<n>In this work, we initiate a study of the power of quantum iO.
• Score: 8.093227427119325
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Indistinguishability obfuscation (iO) has emerged as a powerful cryptographic primitive with many implications. While classical iO, combined with the infinitely-often worst-case hardness of $\mathsf{NP}$, is known to imply one-way functions (OWFs) and a range of advanced cryptographic primitives, the cryptographic implications of quantum iO remain poorly understood. In this work, we initiate a study of the power of quantum iO. We define several natural variants of quantum iO, distinguished by whether the obfuscation algorithm, evaluation algorithm, and description of obfuscated program are classical or quantum. For each variant, we identify quantum cryptographic primitives that can be constructed under the assumption of quantum iO and the infinitely-often quantum worst-case hardness of $\mathsf{NP}$ (i.e., $\mathsf{NP} \not\subseteq \mathsf{i.o.BQP}$). In particular, we construct pseudorandom unitaries, QCCC quantum public-key encryption and (QCCC) quantum symmetric-key encryption, and several primitives implied by them such as one-way state generators, (efficiently-verifiable) one-way puzzles, and EFI pairs, etc. While our main focus is on quantum iO, even in the classical setting, our techniques yield a new and arguably simpler construction of OWFs from classical (imperfect) iO and the infinitely-often worst-case hardness of $\mathsf{NP}$.

Related papers

• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Founding Quantum Cryptography on Quantum Advantage, or, Towards Cryptography from $\mathsf{\#P}$-Hardness [10.438299411521099]
  Recent separations have raised the tantalizing possibility of building quantum cryptography from sources of hardness that persist even if hierarchy collapses. We show that quantum cryptography can be based on the extremely mild assumption that $mathsfP#P notsubseteq mathsf(io)BQP/qpoly$.
  arXiv  Detail & Related papers  (2024-09-23T17:45:33Z)
• Sum-of-Squares inspired Quantum Metaheuristic for Polynomial Optimization with the Hadamard Test and Approximate Amplitude Constraints [76.53316706600717]
  Recently proposed quantum algorithm arXiv:2206.14999 is based on semidefinite programming (SDP) We generalize the SDP-inspired quantum algorithm to sum-of-squares. Our results show that our algorithm is suitable for large problems and approximate the best known classicals.
  arXiv  Detail & Related papers  (2024-08-14T19:04:13Z)
• Quantum Truncated Differential and Boomerang Attack [10.853582091917236]
  In this article, we concentrate on truncated differential and boomerang cryptanalysis. We first present a quantum algorithm which is designed for finding truncated differentials of symmetric ciphers. We prove that, with a overwhelming probability, the truncated differentials output by our algorithm must have high differential probability for the vast majority of keys in key space.
  arXiv  Detail & Related papers  (2024-07-21T11:34:29Z)
• Revocable Cryptography from Learning with Errors [61.470151825577034]
  We build on the no-cloning principle of quantum mechanics and design cryptographic schemes with key-revocation capabilities. We consider schemes where secret keys are represented as quantum states with the guarantee that, once the secret key is successfully revoked from a user, they no longer have the ability to perform the same functionality as before.
  arXiv  Detail & Related papers  (2023-02-28T18:58:11Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Quantum Pseudorandomness and Classical Complexity [0.08158530638728499]
  We show that cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist. We discuss implications of these results for cryptography, complexity theory, and quantum tomography.
  arXiv  Detail & Related papers  (2021-03-16T20:54:12Z)
• Quantum Garbled Circuits [9.937090317971313]
  We show how to compute an encoding of a given quantum circuit and quantum input, from which it is possible to derive the output of the computation and nothing else. Our protocol has the so-called $Sigma$ format with a single-bit challenge, and allows the inputs to be delayed to the last round.
  arXiv  Detail & Related papers  (2020-06-01T17:07:01Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.