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Quantum Random Oracle Model with Auxiliary Input

  • Minki HhanEmail author
  • Keita Xagawa
  • Takashi Yamakawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11921)

Abstract

The random oracle model (ROM) is an idealized model where hash functions are modeled as random functions that are only accessible as oracles. Although the ROM has been used for proving many cryptographic schemes, it has (at least) two problems. First, the ROM does not capture quantum adversaries. Second, it does not capture non-uniform adversaries that perform preprocessings. To deal with these problems, Boneh et al. (Asiacrypt’11) proposed using the quantum ROM (QROM) to argue post-quantum security, and Unruh (CRYPTO’07) proposed the ROM with auxiliary input (ROM-AI) to argue security against preprocessing attacks. However, to the best of our knowledge, no work has dealt with the above two problems simultaneously.

In this paper, we consider a model that we call the QROM with (classical) auxiliary input (QROM-AI) that deals with the above two problems simultaneously and study security of cryptographic primitives in the model. That is, we give security bounds for one-way functions, pseudorandom generators, (post-quantum) pseudorandom functions, and (post-quantum) message authentication codes in the QROM-AI.

We also study security bounds in the presence of quantum auxiliary inputs. In other words, we show a security bound for one-wayness of random permutations (instead of random functions) in the presence of quantum auxiliary inputs. This resolves an open problem posed by Nayebi et al. (QIC’15). In a context of complexity theory, this implies \( \mathsf {NP}\cap \mathsf {coNP} \not \subseteq \mathsf {BQP/qpoly}\) relative to a random permutation oracle, which also answers an open problem posed by Aaronson (ToC’05).

Notes

Acknowledgment

We thank anonymous reviewers of Asiacrypt 2019 and Andreas Hülsing for their helpful comments. Minki Hhan was partially supported by the Institute for Information & Communications Technology Promotion (IITP) Grant through the Korean Government (MSIT), (Development of lattice-based post-quantum public-key cryptographic schemes), under Grant 2017-0-00616 and by the Samsung Research Funding Center of Samsung Electronics under Project SRFC-TB1403-52.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.Seoul National UniversitySeoulRepublic of Korea
  2. 2.NTT Secure Platform LaboratoriesTokyoJapan

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