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Cuckoo Commitments: Registration-Based Encryption and Key-Value Map Commitments for Large Spaces

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14442))

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Abstract

Registration-Based Encryption (RBE) [Garg et al. TCC’18] is a public-key encryption mechanism in which users generate their own public and secret keys, and register their public keys with a central authority called the key curator. Similarly to Identity-Based Encryption (IBE), in RBE users can encrypt by only knowing the public parameters and the public identity of the recipient. Unlike IBE, though, RBE does not suffer the key escrow problem—one of the main obstacles of IBE’s adoption in practice—since the key curator holds no secret.

In this work, we put forward a new methodology to construct RBE schemes that support large users identities (i.e., arbitrary strings). Our main result is the first efficient pairing-based RBE for large identities. Prior to our work, the most efficient RBE is that of [Glaeser et al. ePrint’22] which only supports small identities. The only known RBE schemes with large identities are realized either through expensive non-black-box techniques (ciphertexts of 3.6 TB for 1000 users), via a specialized lattice-based construction [Döttling et al. Eurocrypt’23] (ciphertexts of 2.4 GB), or through the more complex notion of Registered Attribute-Based Encryption [Hohenberger et al. Eurocrypt’23]. By unlocking the use of pairings for RBE with large identity space, we enable a further improvement of three orders of magnitude, as our ciphertexts for a system with 1000 users are 1.7 MB.

The core technique of our approach is a novel use of cuckoo hashing in cryptography that can be of independent interest. We give two main applications. The first one is the aforementioned RBE methodology, where we use cuckoo hashing to compile an RBE with small identities into one for large identities. The second one is a way to convert any vector commitment scheme into a key-value map commitment. For instance, this leads to the first algebraic pairing-based key-value map commitments.

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Notes

  1. 1.

    Informally, a CH is robust if its correctness error is negligible for adversarially chosen inputs; standard correctness holds only for inputs chosen before public parameters.

  2. 2.

    One can also use polynomial commitments, e.g., [42], in combination with interpolation but to the best of our knowledge this KVC is not updatable.

  3. 3.

    We note that if \(\boldsymbol{T}[\textsf{id}^{(\eta )}] \ne \textsf{id}\) then from position-binding of the VC no PPT party can compute a \(\varPsi \) that verifies for \(\textsf{id}\) in position \(\textsf{id}^{(\eta )}\).

  4. 4.

    The update information does not have to be secret and is only computed by KC and not by the user for efficiency.

  5. 5.

    We consider the identity space \(\{0,1\}^{2 \lambda }\) virtually unbounded since one can always use a collision-resistant hash function \(H: \{0, 1\}^{*} \rightarrow \{0, 1\}^{2 \lambda }\) to support unbounded identities.

  6. 6.

    In case the VC is updatable, the updated D can computed efficiently without having to recompute it from scratch. For simplicity we do not make this explicit in the construction.

  7. 7.

    The \(\log k = \log \lambda \) factor is in bits, while the rest are in cryptographic elements (e.g. Group elements or Lattice matrices) therefore \(\log \lambda \) bits correspond to one element.

  8. 8.

    In [24] \(\mathcal{I}\mathcal{D}\) can be arbitrarily large. We make use of the scheme with small identities to argue that compiling it to a large \(\mathcal{I}\mathcal{D}\) with our transformation instead can benefit efficiency.

  9. 9.

    In theory, this is integrated in the trusted setup of the CRS generation. In practice, though, this type of CRS is highly undesirable, since no efficient MPC ceremony to generate it is currently known, in contrast to the ’powers-of-tau’ CRS.

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Acknowledgements

We would like to thank Kevin Yeo for helpful feedback on the robustness of Cuckoo Hashing. The first two authors received funding from projects from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under project PICOCRYPT (grant agreement No. 101001283), from the Spanish Government under projects PRODIGY (TED2021-132464B-I00) and ESPADA (PID2022-142290OB-I00). The last two projects are co-funded by European Union EIE, and NextGenerationEU/PRTR funds.

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Authors and Affiliations

  1. IMDEA Software Institute, Madrid, Spain

    Dario Fiore & Dimitris Kolonelos

  2. Universidad Politénica de Madrid, Madrid, Spain

    Dimitris Kolonelos

  3. DIENS, École Normale Supérieure, CNRS, Inria, Université PSL, Paris, France

    Paola de Perthuis

  4. Cosmian, Paris, France

    Paola de Perthuis

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  1. Dario Fiore
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  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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Fiore, D., Kolonelos, D., Perthuis, P.d. (2023). Cuckoo Commitments: Registration-Based Encryption and Key-Value Map Commitments for Large Spaces. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14442. Springer, Singapore. https://doi.org/10.1007/978-981-99-8733-7_6

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