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Adaptively Single-Key Secure Constrained PRFs for \(\mathrm {NC}^1\)

  • Nuttapong Attrapadung
  • Takahiro Matsuda
  • Ryo Nishimaki
  • Shota Yamada
  • Takashi YamakawaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11443)

Abstract

We present a construction of an adaptively single-key secure constrained PRF (CPRF) for \(\mathbf {NC}^1\) assuming the existence of indistinguishability obfuscation (IO) and the subgroup hiding assumption over a (pairing-free) composite order group. This is the first construction of such a CPRF in the standard model without relying on a complexity leveraging argument.

To achieve this, we first introduce the notion of partitionable CPRF, which is a CPRF accommodated with partitioning techniques and combine it with shadow copy techniques often used in the dual system encryption methodology. We present a construction of partitionable CPRF for \(\mathbf {NC}^1\) based on IO and the subgroup hiding assumption over a (pairing-free) group. We finally prove that an adaptively single-key secure CPRF for \(\mathbf {NC}^1\) can be obtained from a partitionable CPRF for \(\mathbf {NC}^1\) and IO.

Notes

Acknowledgments

We would like to thank Yilei Chen for the valuable discussion about adaptive security of the LWE-based constraint-hiding CPRFs. The first, second, and fourth authors were supported by JST CREST Grant Number JPMJCR1688, Japan.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Nuttapong Attrapadung
    • 1
  • Takahiro Matsuda
    • 1
  • Ryo Nishimaki
    • 2
  • Shota Yamada
    • 1
  • Takashi Yamakawa
    • 2
    Email author
  1. 1.National Institute of Advanced Industrial Science and Technology (AIST)TokyoJapan
  2. 2.NTT Secure Platform LaboratoriesTokyoJapan

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