One-Wayness in Quantum Cryptography

• URL: http://arxiv.org/abs/2210.03394v3
• Date: Wed, 8 May 2024 02:31:38 GMT
• Title: One-Wayness in Quantum Cryptography
• Authors: Tomoyuki Morimae, Takashi Yamakawa,
• Abstract summary: We study properties of one-way state generators (OWSGs), which are a quantum analogue of one-way functions. We show that Quantum digital signatures are equivalent to OWSGs. We introduce an variant of OWSGs, which we call secretly-verifiable and statistically-invertible OWSGs.
• Score: 9.09597656634436
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The existence of one-way functions is one of the most fundamental assumptions in classical cryptography. In the quantum world, on the other hand, there are evidences that some cryptographic primitives can exist even if one-way functions do not exist. We therefore have the following important open problem in quantum cryptography: What is the most fundamental element in quantum cryptography? In this direction, Brakerski, Canetti, and Qian recently defined a notion called EFI pairs, which are pairs of efficiently generatable states that are statistically distinguishable but computationally indistinguishable, and showed its equivalence with some cryptographic primitives including commitments, oblivious transfer, and general multi-party computations. However, their work focuses on decision-type primitives and does not cover search-type primitives like quantum money and digital signatures. In this paper, we study properties of one-way state generators (OWSGs), which are a quantum analogue of one-way functions. We first revisit the definition of OWSGs and generalize it by allowing mixed output states. Then we show the following results. (1) We define a weaker version of OWSGs, weak OWSGs, and show that they are equivalent to OWSGs. (2) Quantum digital signatures are equivalent to OWSGs. (3) Private-key quantum money schemes (with pure money states) imply OWSGs. (4) Quantum pseudo one-time pad schemes imply both OWSGs and EFI pairs. (5) We introduce an incomparable variant of OWSGs, which we call secretly-verifiable and statistically-invertible OWSGs, and show that they are equivalent to EFI pairs.

Related papers

• Revocable Encryption, Programs, and More: The Case of Multi-Copy Security [48.53070281993869]
  We show the feasibility of revocable primitives, such as revocable encryption and revocable programs. This suggests that the stronger notion of multi-copy security is within reach in unclonable cryptography.
  arXiv  Detail & Related papers  (2024-10-17T02:37:40Z)
• A New World in the Depths of Microcrypt: Separating OWSGs and Quantum Money from QEFID [16.5193119873963]
  We show that there is a quantum unitary oracle relative to which EFI pairs exist, but OWSGs do not. We separate, via our oracle, QEFID, and one-way puzzles from OWSGs and several other Microcrypt primitives.
  arXiv  Detail & Related papers  (2024-10-04T14:11:56Z)
• Oracle Separation Between Quantum Commitments and Quantum One-wayness [0.6882042556551611]
  We show that there exists a unitary quantum oracle relative to which quantum commitments exist but no (efficiently verifiable) one-way state generators exist. Recent work has shown that commitments can be constructed from one-way state generators, but the other direction has remained open.
  arXiv  Detail & Related papers  (2024-10-04T12:26:21Z)
• Pseudo-Entanglement is Necessary for EFI Pairs [0.0]
  We consider a new quantum resource, pseudo-entanglement, and show that the existence of EFI pairs implies the existence of pseudo-entanglement. Our result has important implications for the field of computational cryptography.
  arXiv  Detail & Related papers  (2024-06-11T01:44:16Z)
• Exponential Quantum One-Wayness and EFI Pairs [18.481934628015004]
  In classical cryptography, one-way functions are widely considered to be the minimal computational assumption. There are currently two major candidates for the minimal assumption: the search quantum generalization of one-way functions are one-way state generators (OWSG) We show that IV-OWSGs are precisely equivalent to EFI pairs, with an exponential loss in the reduction.
  arXiv  Detail & Related papers  (2024-04-21T15:55:00Z)
• Commitments from Quantum One-Wayness [0.0]
  This work studies one-way state generators, a natural quantum relaxation of one-way functions. A fundamental question is whether this type of quantum one-wayness suffices to realize quantum cryptography. We prove that one-way state generators with pure state outputs imply quantum bit commitments and secure multiparty computation.
  arXiv  Detail & Related papers  (2023-10-17T18:48:22Z)
• Publicly-Verifiable Deletion via Target-Collapsing Functions [81.13800728941818]
  We show that targetcollapsing enables publiclyverifiable deletion (PVD) We build on this framework to obtain a variety of primitives supporting publiclyverifiable deletion from weak cryptographic assumptions.
  arXiv  Detail & Related papers  (2023-03-15T15:00:20Z)
• 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 Proofs of Deletion for Learning with Errors [91.3755431537592]
  We construct the first fully homomorphic encryption scheme with certified deletion. Our main technical ingredient is an interactive protocol by which a quantum prover can convince a classical verifier that a sample from the Learning with Errors distribution in the form of a quantum state was deleted.
  arXiv  Detail & Related papers  (2022-03-03T10:07:32Z)
• Secure Two-Party Quantum Computation Over Classical Channels [63.97763079214294]
  We consider the setting where the two parties (a classical Alice and a quantum Bob) can communicate only via a classical channel. We show that it is in general impossible to realize a two-party quantum functionality with black-box simulation in the case of malicious quantum adversaries. We provide a compiler that takes as input a classical proof of quantum knowledge (PoQK) protocol for a QMA relation R and outputs a zero-knowledge PoQK for R that can be verified by classical parties.
  arXiv  Detail & Related papers  (2020-10-15T17:55:31Z)
• Quantum copy-protection of compute-and-compare programs in the quantum random oracle model [48.94443749859216]
  We introduce a quantum copy-protection scheme for a class of evasive functions known as " compute-and-compare programs" We prove that our scheme achieves non-trivial security against fully malicious adversaries in the quantum random oracle model (QROM) As a complementary result, we show that the same scheme fulfils a weaker notion of software protection, called "secure software leasing"
  arXiv  Detail & Related papers  (2020-09-29T08:41:53Z)

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.