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Broadcast Encryption with Size \(N^{1/3}\) and More from k-Lin

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Advances in Cryptology – CRYPTO 2021 (CRYPTO 2021)

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Abstract

We present the first pairing-based ciphertext-policy attribute-based encryption (CP-ABE) scheme for the class of degree 3 polynomials with compact parameters: the public key, ciphertext and secret keys comprise O(n) group elements, where n is input length for the function. As an immediate corollary, we obtain a pairing-based broadcast encryption scheme for N users with \(O(N^{1/3})\)-sized parameters, breaking the long-standing \(\sqrt{N}\) barrier for pairing-based broadcast encryption. All of our constructions achieve adaptive security against unbounded collusions, and rely on the (bilateral) k-Lin assumption in prime-order bilinear groups.

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Acknowledgments

I am extremely grateful to Junqing Gong for meticulous proof-reading and constructive feedback. I would also like to thank Tianren Liu for helpful discussions on the challenges of extending our \(N^{1/3}\) CDS scheme in [22] to general fields while preserving degree 2 reconstruction.

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Authors and Affiliations

  1. NTT Research, California, USA

    Hoeteck Wee

  2. ENS, Paris, France

    Hoeteck Wee

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  1. Hoeteck Wee
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Correspondence to Hoeteck Wee .

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Editors and Affiliations

  1. Columbia University, New York City, NY, USA

    Tal Malkin

  2. University of Michigan, Ann Arbor, MI, USA

    Chris Peikert

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Wee, H. (2021). Broadcast Encryption with Size \(N^{1/3}\) and More from k-Lin. In: Malkin, T., Peikert, C. (eds) Advances in Cryptology – CRYPTO 2021. CRYPTO 2021. Lecture Notes in Computer Science(), vol 12828. Springer, Cham. https://doi.org/10.1007/978-3-030-84259-8_6

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  • DOI: https://doi.org/10.1007/978-3-030-84259-8_6

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