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(Tightly) QCCA-Secure Key-Encapsulation Mechanism in the Quantum Random Oracle Model

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Post-Quantum Cryptography (PQCrypto 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11505))

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Abstract

This paper studies indistinguishability against quantum chosen-ciphertext attacks (IND-qCCA security) of key-encapsulation mechanisms (KEMs) in quantum random oracle model (QROM). We show that the SXY conversion proposed by Saito, Yamakawa, and Xagawa (EUROCRYPT 2018) and the HU conversion proposed by Jiang, Zhang, and Ma (PKC 2019) turn a weakly-secure deterministic public-key encryption scheme into an IND-qCCA-secure KEM scheme in the QROM. The proofs are very similar to that for the IND-CCA security in the QROM, easy to understand, and as tight as the original proofs.

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Notes

  1. 1.

    We also note that Anand, Targhi, Tabia, and Unruh [ATTU16] showed several modes are secure against quantum superposition attacks if the underlying block cipher is quantumly-secure PRF.

  2. 2.

    This means that if there is quantum chosen-plaintext or quantum chosen-ciphertext attack that breaks a cryptographic scheme easily, we should not publish an obfuscated code by the white-box cryptography or obfuscation.

  3. 3.

    Boneh et al. [BDF+11] defined history-free reductions for signature schemes. They also discussed the difficulties to model history-free reductions in the case of (public-key) encryption schemes. We also do not define history-free property of reductions for KEMs.

  4. 4.

    Any efficient adversary cannot distinguish \(E(k,m_0)\) from \(E(k,m_1)\) even if it chooses \(m_0\) and \(m_1\) with .

  5. 5.

    We allow a reduction algorithm to access the random oracles. See Subsect. 2.2 for details.

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Acknowledgments

We would like to thank Haodong Jiang and anonymous reviewers of PQCrypto 2019 for insightful comments.

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Authors and Affiliations

  1. NTT Secure Platform Laboratories, 3-9-11, Midori-cho, Musashino-shi, Tokyo, 180-8585, Japan

    Keita Xagawa & Takashi Yamakawa

Authors
  1. Keita Xagawa
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  2. Takashi Yamakawa
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Corresponding author

Correspondence to Keita Xagawa .

Editor information

Editors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, USA

    Jintai Ding

  2. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA

    Rainer Steinwandt

A Simple Lemma

A Simple Lemma

Lemma A.1

For any reals a, b, and c with \(c \ge 0\), we have

Proof

We consider the three cases below:

  • Case \(a-b \ge c \ge 0\): In this case, we have \(a-b-c \ge 0\). Thus, we have .

  • Case \(a-b \le 0 \le c\): In this case, we have \(a-b-c \le 0\). We have .

  • Case \(0 \le a-b \le c\): Again, we have \(a-b-c \le 0\). We have .

In all three cases, we have as we wanted.    \(\square \)

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Xagawa, K., Yamakawa, T. (2019). (Tightly) QCCA-Secure Key-Encapsulation Mechanism in the Quantum Random Oracle Model. In: Ding, J., Steinwandt, R. (eds) Post-Quantum Cryptography. PQCrypto 2019. Lecture Notes in Computer Science(), vol 11505. Springer, Cham. https://doi.org/10.1007/978-3-030-25510-7_14

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  • DOI: https://doi.org/10.1007/978-3-030-25510-7_14

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