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Optimizing Registration Based Encryption

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Cryptography and Coding (IMACC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13129))

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Abstract

The recent work of Garg et al. from TCC’18 introduced the notion of registration based encryption (RBE). The principal motivation behind RBE is to address the key escrow issue of identity based encryption (IBE), where an IBE authority is trusted to generate private keys for all users in the system. Although RBE has excellent asymptotic properties, it is currently impractical; in our estimate, ciphertext size would be about 11 TB in an RBE deployment supporting 2 billion users.

Motivated by this observation, our work attempts to reduce the concrete communication and computation cost of the current state-of-the-art construction. Our contribution is two-fold. First, we replace the usage of Merkle trees in RBE with crit-bit trees, a form of PATRICIA trie, without relaxing any of the original efficiency requirements introduced by Garg et al. This change reduces the ciphertext size by 15% and the computation cost of decryption by 30%. Second, we observe that increasing RBE’s public parameters by a few hundred kilobytes could reduce the ciphertext size by an additional 50%. Overall, our work decreases the ciphertext size by 57.5%.

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Notes

  1. 1.

    WhatsApp implements end-to-end encryption and has 2 billion users [13].

  2. 2.

    Free-XOR [26] is an optimization for garbled circuits which allows the garbler to create the garbled truth table “for free”, without symmetric key operations.

  3. 3.

    We assume the identities can be ordered.

  4. 4.

    If \(\mathcal {C}\) stores a tuple, it means appending the tuple to \(\mathcal {C}\)’s local state so that it can be accessed later.

  5. 5.

    A path is valid when the adjacent nodes obey the hash-pointer constraint.

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Acknowledgments

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 (Approved for Public Release, Distribution Unlimited), 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 & Nigel P. Smart

  2. SRI International, Menlo Park, CA, USA

    Karim Eldefrawy

  3. Department of Computer Science, University of Bristol, Bristol, UK

    Nigel P. Smart

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  1. Kelong Cong
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Correspondence to Nigel P. Smart .

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  1. Economics, Mathematics and Statistics, University of London Birkbeck, London, UK

    Maura B. Paterson

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Cong, K., Eldefrawy, K., Smart, N.P. (2021). Optimizing Registration Based Encryption. In: Paterson, M.B. (eds) Cryptography and Coding. IMACC 2021. Lecture Notes in Computer Science(), vol 13129. Springer, Cham. https://doi.org/10.1007/978-3-030-92641-0_7

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