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International Conference on Cryptology and Information Security in Latin America

LATINCRYPT 2021: Progress in Cryptology – LATINCRYPT 2021 pp 320–340Cite as

LOVE a Pairing

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12912))

Abstract

The problem of securely outsourcing the computation of a bilinear pairing has been widely investigated in the literature. Designing an efficient protocol with the desired functionality has, however, been an open challenge for a long time. Recently, Di Crescenzo et al. (CARDIS’20) proposed the first suite of protocols for securely and efficiently delegating pairings with online inputs under the presence of a malicious server. We progress along this path with the aim of LOVE (Lowering the cost of Outsourcing and Verifying Efficiently) a pairing. Our contributions are threefold. First, we propose a protocol (LOVE) that improves the efficiency of Di Crescenzo et al.’s proposal for securely delegating pairings with online, public inputs. Second, we provide the first implementation of efficient protocols in this setting. Finally, we evaluate the performance of our LOVE protocol in different application scenarios by benchmarking an implementation using BN, BLS12 and BLS24 pairing-friendly curves. Interestingly, compared to Di Crescenzo et al.’s protocol, LOVE is up to 29.7% faster for the client, up to 24.9% for the server and requires 23–24% less communication cost depending on the choice of parameters. Furthermore, we note that our LOVE protocol is especially suited for subgroup-secure groups: checking the correctness of the delegated pairing requires up to 56.2% less computations than evaluating the pairing locally (no delegation). This makes LOVE the most efficient protocol to date for securely outsourcing the computation of a pairing with online public inputs, even when the server is malicious.

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Notes

  1. 1.

    Following the definition given in [38], a curve is said to be \(\mathbb {G}_T\)-strong, if \(\phi _k(p)/q \) does not have small factors.

  2. 2.

    The resulting code is available in the library repository for reproducibility.

  3. 3.

    https://github.com/miracl/MIRACL/.

  4. 4.

    https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-bls-signature-04.

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Acknowledgments

This work was partly funded by:the strategic research area ELLIIT. The first author is also affiliated to the DIGIT Centre for Digitalisation, Big Data and Data Analytics; and the Concordium Blockchain Research Center at Aarhus University.

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Authors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Diego F. Aranha

  2. Lund University, Lund, Sweden

    Elena Pagnin

  3. Cryptography Research Centre, Technology Innovation Institute, Abu Dhabi, UAE

    Francisco Rodríguez-Henríquez

  4. Computer Science Department, Cinvestav, Mexico

    Diego F. Aranha, Elena Pagnin & Francisco Rodríguez-Henríquez

Authors
  1. Diego F. Aranha
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  2. Elena Pagnin
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  3. Francisco Rodríguez-Henríquez
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Correspondence to Diego F. Aranha .

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Editors and Affiliations

  1. Microsoft Research, Redmond, WA, USA

    Patrick Longa

  2. Universitat Pompeu Fabra, Barcelona, Spain

    Carla Ràfols

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Aranha, D.F., Pagnin, E., Rodríguez-Henríquez, F. (2021). LOVE a Pairing. In: Longa, P., Ràfols, C. (eds) Progress in Cryptology – LATINCRYPT 2021. LATINCRYPT 2021. Lecture Notes in Computer Science(), vol 12912. Springer, Cham. https://doi.org/10.1007/978-3-030-88238-9_16

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