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Paper: Adaptively Single-Key Secure Constrained PRFs for $\mathrm {NC}^1$

Authors:
Nuttapong Attrapadung
Takahiro Matsuda
Ryo Nishimaki
Shota Yamada
Takashi Yamakawa
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DOI: 10.1007/978-3-030-17259-6_8
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Conference: PKC 2019
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.
BibTeX
@inproceedings{pkc-2019-29302,
  title={Adaptively Single-Key Secure Constrained PRFs for $$\mathrm {NC}^1$$},
  booktitle={Public-Key Cryptography – PKC 2019},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={11443},
  pages={223-253},
  doi={10.1007/978-3-030-17259-6_8},
  author={Nuttapong Attrapadung and Takahiro Matsuda and Ryo Nishimaki and Shota Yamada and Takashi Yamakawa},
  year=2019
}