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Lossy Algebraic Filters with Short Tags

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Public-Key Cryptography – PKC 2019 (PKC 2019)

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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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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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