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Strong accumulators from collision-resistant hashing

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Abstract

Accumulator schemes were introduced in order to represent a large set of values as one short value called the accumulator. These schemes allow one to generate membership proofs, that is, short witnesses that a certain value belongs to the set. In universal accumulator schemes, efficient proofs of non-membership can also be created. Li et al. (Proceedings of applied cryptography and network security—ACNS ’07, LNCS, vol 4521, 2007), building on the work of Camenisch and Lysyanskaya (Advances in cryptology—proceedings of Crypto ’02, LNCS, vol 2442. Springer, Berlin, pp 61–76, 2002), proposed an efficient accumulator scheme, which relies on a trusted accumulator manager. Specifically, a manager that correctly performs accumulator updates. In this work, we introduce the notion of strong universal accumulator schemes, which are similar in functionality to universal accumulator schemes, but do not assume the accumulator manager is trusted. We also formalize the security requirements for such schemes. We then give a simple construction of a strong universal accumulator scheme, which is provably secure under the assumption that collision-resistant hash functions exist. The weaker requirement on the accumulator manager comes at a price; our scheme is less efficient than known universal accumulator schemes—the size of (non)membership witnesses is logarithmic in the size of the accumulated set in contrast to constant in the scheme of Camenisch and Lysyanskaya. Finally, we show how to use strong universal accumulators to solve a problem of practical relevance, the so-called e-Invoice Factoring Problem.

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Authors and Affiliations

  1. Department of Computer Science, University of Chile, Blanco Encalada 2120, 3er piso, Santiago, Chile

    Philippe Camacho & Alejandro Hevia

  2. Depto. Ing. Matemática and Ctr. Modelamiento Matemático UMI 2807, U. Chile, Santiago, Chile

    Marcos Kiwi

  3. CEO khipu.com, Santiago, Chile

    Roberto Opazo

Authors
  1. Philippe Camacho
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  2. Alejandro Hevia
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  3. Marcos Kiwi
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  4. Roberto Opazo
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Corresponding author

Correspondence to Alejandro Hevia.

Additional information

A preliminary version of this work appeared in proceedings of the 11th Information Security Conference, ISC’08, Lecture Notes in Computer Science 5222, pages 471–486, Springer-Verlag, 2008. Mr. Camacho gratefully acknowledges the support of CONICYT via FONDAP en Matemáticas Aplicadas. Mr. Hevia gratefully acknowledges the support of CONICYT via FONDECYT No. 1070332. Mr. Kiwi is supported by CONICYT via FONDECYT No. 1010689 and FONDAP-Basal in Applied Mathematics, and Millenium Nucleus Information and Coordination in Networks ICM/FIC P10-024F.

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Camacho, P., Hevia, A., Kiwi, M. et al. Strong accumulators from collision-resistant hashing. Int. J. Inf. Secur. 11, 349–363 (2012). https://doi.org/10.1007/s10207-012-0169-2

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