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New code-based cryptographic accumulator and fully dynamic group signature

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Abstract

A cryptographic accumulator is a cryptographic primitive which produces a succinct aggregate of a set of elements. This type of scheme allows to produce a membership proof for each element of the set. In this paper, we propose a code-based cryptographic accumulator that is quantum computer resistant. Specifically, our scheme is based on the hardness of the Syndrome Decoding problem and satisfies the collision freeness and indistinguishability requirements. We also use double circulant codes which allow us to get a small key size, especially we get for an 80 bits security a small public key of 347 bits. Furthermore, we use the proposed cryptographic accumulator to create a fully dynamic code-based group signature. Moreover, we give an implementation of our scheme which is, to the best of our knowledge, the first direct implementation of a post-quantum cryptographic accumulator.

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Acknowledgements

Authors would like to express their acknowledgement and deep gratitude to the reviewers for their insightful comments, constructive remarks and efforts towards improving this paper. Authors are also grateful to Dr. Maryem Ait El Hadj who did a wonderful job in re-reading and providing language help.

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  1. Laboratory of Mathematics, Computer Science, Applications and Information Security, Faculty of Sciences, Mohammed V University in Rabat, BP 1014 RP, Rabat, Morocco

    Edoukou Berenger Ayebie & El Mamoun Souidi

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  1. Edoukou Berenger Ayebie
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  2. El Mamoun Souidi
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”

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Ayebie, E.B., Souidi, E.M. New code-based cryptographic accumulator and fully dynamic group signature. Des. Codes Cryptogr. 90, 2861–2891 (2022). https://doi.org/10.1007/s10623-022-01007-5

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