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Cryptographic Accumulators: New Definitions, Enhanced Security, and Delegatable Proofs

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Progress in Cryptology - AFRICACRYPT 2024 (AFRICACRYPT 2024)

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Abstract

Cryptographic accumulators, introduced in 1993 by Benaloh and De Mare, represent a set with a concise value and offer proofs of (non-)membership. Accumulators have evolved, becoming essential in anonymous credentials, e-cash, and blockchain applications. Various properties like dynamic and universal emerged for specific needs, leading to multiple accumulator definitions. In 2015, Derler, Hanser, and Slamanig proposed a unified model, but new properties, including zero-knowledge security, have arisen since. We offer a new definition of accumulators, based on Derler et al.’s, that is suitable for all properties. We also introduce a new security property, unforgeability of private evaluation, to protect accumulator from forgery and we verify this property in Barthoulot, Blazy, and Canard’s recent accumulator. Finally we provide discussions on security properties of accumulators and on the delegatable (non-)membership proofs property.

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Notes

  1. 1.

    In some works, “collision resistance” is called “collision freeness”, “soundness” or “set binding” [22]. We will only use the terms collision resistance in the following.

  2. 2.

    Applying a single action applied to n items instead of one action per item.

  3. 3.

    [55] introduced the chosen element attack (CEA) to characterize collision resistance in dynamic accumulators. Notice that this term has been discontinued or abandoned.

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Acknowledgement

The authors would like to thank anonymous reviewers for their helpful discussions and valuable comments. This work is supported in part by the Banque Publique d’Investissement under the VisioConfiance project and the French ANR SANGRIA project (ANR-21-CE39-0006).

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Authors and Affiliations

  1. Université de Montpellier, LIRMM, Montpellier, France

    Anaïs Barthoulot

  2. École Polytechnique, Palaiseau, France

    Olivier Blazy

  3. LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France

    Sébastien Canard

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  1. Anaïs Barthoulot
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  2. Olivier Blazy
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  3. Sébastien Canard
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Correspondence to Anaïs Barthoulot .

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Editors and Affiliations

  1. Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Serge Vaudenay

  2. University of Birmingham, Birmingham, UK

    Christophe Petit

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Barthoulot, A., Blazy, O., Canard, S. (2024). Cryptographic Accumulators: New Definitions, Enhanced Security, and Delegatable Proofs. In: Vaudenay, S., Petit, C. (eds) Progress in Cryptology - AFRICACRYPT 2024. AFRICACRYPT 2024. Lecture Notes in Computer Science, vol 14861. Springer, Cham. https://doi.org/10.1007/978-3-031-64381-1_5

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