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Efficient Asynchronous Accumulators for Distributed PKI

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Security and Cryptography for Networks (SCN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9841))

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Abstract

Cryptographic accumulators are a tool for compact set representation and secure set membership proofs. When an element is added to a set by means of an accumulator, a membership witness is generated. This witness can later be used to prove the membership of the element. Typically, the membership witness has to be synchronized with the accumulator value: it has to be updated every time another element is added to the accumulator, and it cannot be used with outdated accumulator values. However, in many distributed applications (such as blockchain-based public key infrastructures), requiring strict synchronization is prohibitive. We define low update frequency, which means that a witness only needs to be updated a small number of times, and old-accumulator compatibility, which means that a witness can be used with outdated accumulator values. Finally, we propose an accumulator that achieves both of those properties.

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Notes

  1. 1.

    The question of whether accumulators updates can be batched, as in our scheme, was first posed by Fazio and Nicolosi [12] in the context of dynamic accumulators, which support deletions. It was answered in the negative by Camacho [6], but only in the context of deletions, and only in the centralized case (when all witnesses are updated by the same entity).

  2. 2.

    Note that we do not address public key updates; see Yakoubov et al. [22] for a discussion of such updates.

  3. 3.

    There also exist universal accumulators [14] which additionally support proofs of non-membership; however, we only consider proofs of membership in this paper.

  4. 4.

    Note that this does not compromise the soundness property of the accumulator, because if \(x\) was not a member of the accumulator at \(t_{a}\), \(w_{t}^{x}\) does not verify with \(a_{t_{a}}\).

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Acknowledgements

This research is supported, in part, by US NSF grants CNS-1012910, CNS-1012798, and CNS-1422965. Leonid Reyzin gratefully acknowledges the hospitality of IST Austria and École normale supérieure, where part of this work was performed.

The authors would like to thank Dimitris Papadopoulos and Foteini Baldimtsi for their insightful feedback.

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Authors and Affiliations

  1. Boston University, Boston, USA

    Leonid Reyzin & Sophia Yakoubov

Authors
  1. Leonid Reyzin
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  2. Sophia Yakoubov
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Corresponding author

Correspondence to Sophia Yakoubov .

Editor information

Editors and Affiliations

  1. Rensselaer Polytechnic Institute, Troy, New York, USA

    Vassilis Zikas

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

A Element Addition

A Element Addition

In Figs. 5 and 6, we illustrate a single element addition. Element \(x_{t+1}\) is being added to the accumulator. The depth 0 and depth 1 Merkle trees are both present in the accumulator, so two “carries” occur before \(x_{t+1}\) is successfully added into the Merkle tree of depth 2.

Fig. 5.
figure 5

An illustration of an addition operation in our accumulator - part 1.

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Fig. 6.
figure 6

An illustration of an addition operation in our accumulator - part 2.

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Reyzin, L., Yakoubov, S. (2016). Efficient Asynchronous Accumulators for Distributed PKI. In: Zikas, V., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2016. Lecture Notes in Computer Science(), vol 9841. Springer, Cham. https://doi.org/10.1007/978-3-319-44618-9_16

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  • DOI: https://doi.org/10.1007/978-3-319-44618-9_16

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  • Online ISBN: 978-3-319-44618-9

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