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Gladius: LWR Based Efficient Hybrid Public Key Encryption with Distributed Decryption

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Advances in Cryptology – ASIACRYPT 2021 (ASIACRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13093))

Abstract

Standard hybrid encryption schemes based on the KEM-DEM framework are hard to implement efficiently in a distributed manner whilst maintaining the CCA security property of the scheme. This is because the DEM needs to be decrypted under the key encapsulated by the KEM, before the whole ciphertext is declared valid. In this paper we present a new variant of the KEM-DEM framework, closely related to Tag-KEMs, which sidesteps this issue. We then present a post-quantum KEM for this framework based on Learning-with-Rounding, which is designed specifically to have fast distributed decryption. Our combined construction of a hybrid encryption scheme with Learning-with-Rounding based KEM, called Gladius, is closely related to the NIST Round 3 candidate called Saber. Finally, we give a prototype distributed implementation that achieves a decapsulation time of 4.99 s for three parties.

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Notes

  1. 1.

    A scheme is defined to be rigid if decryption of a ‘ciphertext’, which is not the output of an encryption operation, always returns \(\perp \).

  2. 2.

    A scheme is said to be PCA (plain-check attack) secure if it is secure in the presence of an oracle which allows the adversary to check whether a given ciphertext encrypts a given plaintext.

  3. 3.

    Although there is an issue of having comparable security for these parameters, due to our reliance on LWE in the key generation phase, see Table 1 for more details.

  4. 4.

    One time meaning that the attacker does not get access to an encryption oracle.

  5. 5.

    https://bitbucket.org/malb/lwe-estimator/src/master/.

  6. 6.

    The result in [12] is only given for normal and Ring LWE/LWR, but extending the result to the module variants is immediate.

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Acknowledgment

We would like to thank Alexandra Boldyreva for clarifying some issues with the PRIV definition of security for deterministic encryption, Frederik Vercauteren for clarifying some issues in relation to Learning-with-Rounding, Andrej Bogdanov for clarifying issues related to the theoretical reductions between LWE and LWR, and Ward Beullens on comments on an earlier draft. This work was supported in part by CyberSecurity Research Flanders with reference number VR20192203, by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. FA8750-19-C-0502, and by the FWO under an Odysseus project GOH9718N. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the ERC, DARPA, the US Government or the FWO. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.

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Authors and Affiliations

  1. imec-COSIC, KU Leuven, Leuven, Belgium

    Kelong Cong, Daniele Cozzo & Nigel P. Smart

  2. ETH Zurich, Zurich, Switzerland

    Varun Maram

  3. University of Bristol, Bristol, UK

    Nigel P. Smart

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  1. Kelong Cong
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Correspondence to Kelong Cong , Daniele Cozzo , Varun Maram or Nigel P. Smart .

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  1. NTT Corporation, Tokyo, Japan

    Mehdi Tibouchi

  2. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

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Cong, K., Cozzo, D., Maram, V., Smart, N.P. (2021). Gladius: LWR Based Efficient Hybrid Public Key Encryption with Distributed Decryption. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13093. Springer, Cham. https://doi.org/10.1007/978-3-030-92068-5_5

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