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Title:
Adaptively Single-Key Secure Constrained PRFs for NC1
Authors: Nuttapong Attrapadung, Takahiro Matsuda, Ryo Nishimaki, Shota Yamada, Takashi Yamakawa
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 \mathrm{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.
ePrint: https://eprint.iacr.org/2018/1000
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