Abstract
Indistinguishability against adaptive chosen-ciphertext attacks (IND-CCA2) is usually considered the most desirable security notion for classical encryption. In this work, we investigate its adaptation in the quantum world, when an adversary can perform superposition queries. The security of quantum-secure classical encryption has first been studied by Boneh and Zhandry (CRYPTO’13), but they restricted the adversary to classical challenge queries, which makes the indistinguishability only hold for classical messages (IND-qCCA2). We extend their work by giving the first security notions for fully quantum indistinguishability under quantum adaptive chosen-ciphertext attacks, where the indistinguishability holds for superposition of plaintexts (qIND-qCCA2).
E. Ebrahimi—Work done while at École Normale Supérieure.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We note that previous works [7, 17] use random permutations instead of random functions in the random world. It is arguable which security definition is the right adaptation of the classical Real-or-Random security definition to the quantum setting. However, the two notions are equivalent if the message space has size superpolynomial. This is because in this case, random functions and random permutations are indistinguishable.
- 2.
For notation consistency, we use the same subscript in compressed oracles as for standard oracles. However, we note that there is no real function \(h\) in the implementation of \(\textsf{CFourierO}\) and its variants.
- 3.
The oracle first computes \(\textsf{FindImage}'\), records the output in some ancilla register, performs the CNOT operation controlled on the output and finally un-compute \(\textsf{FindImage}'\).
References
Alagic, G., Majenz, C., Russell, A., Song, F.: Quantum-access-secure message authentication via blind-unforgeability. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12107, pp. 788–817. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45727-3_27
Anand, M.V., Targhi, E.E., Tabia, G.N., Unruh, D.: Post-quantum security of the CBC, CFB, OFB, CTR, and XTS modes of operation. In: Takagi, T. (ed.) PQCrypto 2016. LNCS, vol. 9606, pp. 44–63. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29360-8_4
Bellare, M., Namprempre, C.: Authenticated encryption: relations among notions and analysis of the generic composition paradigm. J. Cryptol. 21(4), 469–491 (2008)
Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41–69. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_3
Boneh, D., Zhandry, M.: Quantum-secure message authentication codes. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 592–608. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_35
Boneh, D., Zhandry, M.: Secure signatures and chosen ciphertext security in a quantum computing world. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 361–379. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_21
Carstens, T.V., Ebrahimi, E., Tabia, G.N., Unruh, D.: Relationships between quantum IND-CPA notions. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13042, pp. 240–272. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90459-3_9
Chevalier, C., Ebrahimi, E., Vu, Q.-H.: On security notions for encryption in a quantum world. Cryptology ePrint Archive, Report 2020/237 (2020)
Czajkowski, J., Majenz, C., Schaffner, C., Zur, S.: Quantum lazy sampling and game-playing proofs for quantum indifferentiability. Cryptology ePrint Archive, Report 2019/428 (2019)
Damgård, I., Funder, J., Nielsen, J.B., Salvail, L.: Superposition attacks on cryptographic protocols. In: Padró, C. (ed.) ICITS 2013. LNCS, vol. 8317, pp. 142–161. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04268-8_9
Gagliardoni, T., Hülsing, A., Schaffner, C.: Semantic security and indistinguishability in the quantum world. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 60–89. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3_3
Goldreich, O.: Foundations of Cryptography: Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: 28th ACM STOC, pp. 212–219. ACM Press, May 1996
Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the Fujisaki-Okamoto transformation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 341–371. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_12
Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 207–237. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5_8
Kashefi, E., Kent, A., Vedral, V., Banaszek, K.: Comparison of quantum oracles. Phys. Rev. A 65(5), 050304 (2002)
Mossayebi, S., Schack, R.: Concrete security against adversaries with quantum superposition access to encryption and decryption oracles. arXiv preprint arXiv:1609.03780 (2016)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information: 10th Anniversary Edition, 10th edn. Cambridge University Press, Cambridge (2011)
Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: 40th ACM STOC, pp. 187–196. ACM Press, May 2008
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303–332 (1999)
Simon, D.R.: On the power of quantum computation. In: 35th FOCS, pp. 116–123. IEEE Computer Society Press, November 1994
Zhandry, M.: How to construct quantum random functions. In: 53rd FOCS, pp. 679–687. IEEE Computer Society Press, October 2012
Zhandry, M.: How to record quantum queries, and applications to quantum indifferentiability. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 239–268. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_9
Acknowledgments
This work was supported in part by the French ANR project CryptiQ (ANR-18-CE39-0015) and the French Programme d’Investissement d’Avenir under national project RISQ P141580. The authors want to thank Damien Vergnaud, David Pointcheval and Christian Majenz for fruitful discussions, as well as the anonymous reviewers for useful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Chevalier, C., Ebrahimi, E., Vu, QH. (2022). On Security Notions for Encryption in a Quantum World. In: Isobe, T., Sarkar, S. (eds) Progress in Cryptology – INDOCRYPT 2022. INDOCRYPT 2022. Lecture Notes in Computer Science, vol 13774. Springer, Cham. https://doi.org/10.1007/978-3-031-22912-1_26
Download citation
DOI: https://doi.org/10.1007/978-3-031-22912-1_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-22911-4
Online ISBN: 978-3-031-22912-1
eBook Packages: Computer ScienceComputer Science (R0)