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Fine-Grained Cryptography Revisited

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Book cover Advances in Cryptology – ASIACRYPT 2019 (ASIACRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11923))

Abstract

Fine-grained cryptographic primitives are secure against adversaries with bounded resources and can be computed by honest users with less resources than the adversaries. In this paper, we revisit the results by Degwekar, Vaikuntanathan, and Vasudevan in Crypto 2016 on fine-grained cryptography and show the constructions of three key fundamental fine-grained cryptographic primitives: one-way permutations, hash proof systems (which in turn implies a public-key encryption scheme against chosen chiphertext attacks), and trapdoor one-way functions. All of our constructions are computable in \(\mathsf {NC^1}\) and secure against (non-uniform) \(\mathsf {NC^1}\) circuits under the widely believed worst-case assumption \(\mathsf {NC^1}\subsetneq \mathsf{\oplus L/poly}\).

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Notes

  1. 1.

    The one-wayness of g is based on the indistinguishability of the output distributions of \(\hat{f}\) conditioned on \(f(x) = 0\) and \(f(x) =1\), which can be reduced to \(\mathsf {NC^1}\subsetneq \mathsf{\oplus L/poly}\).

  2. 2.

    There is no rigorous proof showing that the separation holds for \(\mathsf {NC^1}\), while it is an evidence that TDF is not easy to achieve.

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Acknowledgements

A part of this work was supported by NTT Secure Platform Laboratories, JST OPERA JPMJOP1612, JST CREST JPMJCR14D6, JSPS KAKENHI JP16H01705, JP17H01695, and the Sichuan Science and Technology Program under Grant 2017GZDZX0002 and 2018GZDZX0006.

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Authors and Affiliations

  1. Tokyo Institute of Technology, Tokyo, Japan

    Shohei Egashira & Keisuke Tanaka

  2. University of Electronic Science and Technology of China, Chengdu, China

    Yuyu Wang

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  1. Shohei Egashira
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Editors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Steven D. Galbraith

  2. Security Fundamentals Lab, NICT, Tokyo, Japan

    Shiho Moriai

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Egashira, S., Wang, Y., Tanaka, K. (2019). Fine-Grained Cryptography Revisited. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11923. Springer, Cham. https://doi.org/10.1007/978-3-030-34618-8_22

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