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Lossy Algebraic Filters with Short Tags

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Public-Key Cryptography – PKC 2019 (PKC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11442))

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Abstract

Lossy algebraic filters (LAFs) are function families where each function is parametrized by a tag, which determines if the function is injective or lossy. While initially introduced by Hofheinz (Eurocrypt 2013) as a technical tool to build encryption schemes with key-dependent message chosen-ciphertext (KDM-CCA) security, they also find applications in the design of robustly reusable fuzzy extractors. So far, the only known LAF family requires tags comprised of \(\varTheta (n^2)\) group elements for functions with input space \(\mathbb {Z}_p^n\), where p is the group order. In this paper, we describe a new LAF family where the tag size is only linear in n and prove it secure under simple assumptions in asymmetric bilinear groups. Our construction can be used as a drop-in replacement in all applications of the initial LAF system. In particular, it can shorten the ciphertexts of Hofheinz’s KDM-CCA-secure public-key encryption scheme by 19 group elements. It also allows substantial space improvements in a recent fuzzy extractor proposed by Wen and Liu (Asiacrypt 2018). As a second contribution, we show how to modify our scheme so as to prove it (almost) tightly secure, meaning that security reductions are not affected by a concrete security loss proportional to the number of adversarial queries.

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Notes

  1. 1.

    The LAF of [25] was described in terms of symmetric pairings but it extends to asymmetric pairings \(e : \mathbb {G}\times \hat{\mathbb {G}} \rightarrow \mathbb {G}_T\) where tags are comprised of elements in \(\mathbb {G}\).

  2. 2.

    While the assumption of Definition 5 is described using O(Q) group elements, it tightly reduces to wD3DH1 and DDH which both take a constant number of group elements to describe.

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Acknowledgements

We thank the reviewers for their careful reading. This work was funded in part by the French ANR ALAMBIC project (ANR-16-CE39-0006).

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Authors and Affiliations

  1. CNRS, Laboratoire LIP, Lyon, France

    Benoît Libert

  2. ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, Inria, UCBL), Lyon, France

    Benoît Libert

  3. Univ Rennes, CNRS, IRISA, Rennes, France

    Chen Qian

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  1. Benoît Libert
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Correspondence to Benoît Libert .

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  1. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  2. Security Research Laboratories, NEC Corporation, Kawasaki, Japan

    Kazue Sako

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Libert, B., Qian, C. (2019). Lossy Algebraic Filters with Short Tags. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11442. Springer, Cham. https://doi.org/10.1007/978-3-030-17253-4_2

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