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Computational Robust (Fuzzy) Extractors for CRS-Dependent Sources with Minimal Min-entropy

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Theory of Cryptography (TCC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13043))

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Abstract

Robust (fuzzy) extractors are very useful for, e.g., authenticated key exchange from a shared weak secret and remote biometric authentication against active adversaries. They enable two parties to extract the same uniform randomness with a “helper” string. More importantly, they have an authentication mechanism built in that tampering of the “helper” string will be detected. Unfortunately, as shown by Dodis and Wichs, in the information-theoretic setting, a robust extractor for an (n, k)-source requires \(k>n/2\), which is in sharp contrast with randomness extractors which only require \(k=\omega (\log n)\). Existing works either rely on random oracles or introduce CRS and work only for CRS-independent sources (even in the computational setting).

In this work, we give a systematic study about robust (fuzzy) extractors for general CRS dependent sources. We show in the information-theoretic setting, the same entropy lower bound holds even in the CRS model; we then show we can have robust extractors in the computational setting for general CRS-dependent source that is only with minimal entropy. We further extend our construction to robust fuzzy extractors. Along the way, we propose a new primitive called \(\kappa \)-MAC, which is unforgeable with a weak key and hides all partial information about the key (both against auxiliary input); it may be of independent interests.

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Notes

  1. 1.

    For the non-fuzzy case, Dodis et al. [9] presented a partial solution in the computational setting. However, their construction only works for a very special source: the sample consists of (w, c) where c is a ciphertext that probabilistically encrypts 0s under w; they further require the source to have any linear fraction of min-entropy. In comparison, we are aiming for general sources that only have minimal super logarithmic entropy. For the fuzzy case, there is no feasibility result at all.

  2. 2.

    Note that secure sketches achieving t error tolerance are also subject to some entropy-rate lower-bounds [14]. However, for almost all error-rate t/n (except a small range), the bound is notably smaller than 1/2.

  3. 3.

    The RO-based MAC (where \(\mathsf {Tag}(w,m)=H(w,m)\) for a random oracle H) employed in Boyen et al.’s robust (fuzzy) extractor [4] captures all above intuitions, and thus it can be considered as a \(\kappa \)-MAC in the random oracle model.

  4. 4.

    The one-time \(\kappa \)-MAC is enough for our purpose; we may generalize our construction to get a full-fledged \(\kappa \)-MAC using multi-message secure DPKE [5], which will require concrete entropy bound on the source though.

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Acknowledgement

Part of the work was done while both authors were at New Jersey Institute of Technology, and Qiang was then supported in part by NSF #1801492.

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Authors and Affiliations

  1. Alibaba Group, Hangzhou, China

    Hanwen Feng

  2. The University of Sydney, Sydney, Australia

    Qiang Tang

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  1. Hanwen Feng
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Correspondence to Qiang Tang .

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Editors and Affiliations

  1. Georgetown University, Washington, WA, USA

    Kobbi Nissim

  2. The University of Texas at Austin, Austin, TX, USA

    Brent Waters

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Feng, H., Tang, Q. (2021). Computational Robust (Fuzzy) Extractors for CRS-Dependent Sources with Minimal Min-entropy. In: Nissim, K., Waters, B. (eds) Theory of Cryptography. TCC 2021. Lecture Notes in Computer Science(), vol 13043. Springer, Cham. https://doi.org/10.1007/978-3-030-90453-1_24

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  • DOI: https://doi.org/10.1007/978-3-030-90453-1_24

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