## Cryptology ePrint Archive: Report 2018/1000

Adaptively Single-Key Secure Constrained PRFs for NC1

Nuttapong Attrapadung and Takahiro Matsuda and Ryo Nishimaki and Shota Yamada and 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.

Category / Keywords: foundations / constrained pseudorandom function, adaptive security, obfuscation

Contact author: yamakawa takashi at lab ntt co jp, nishimaki ryo@lab ntt co jp, n attrapadung@aist go jp, t-matsuda@aist go jp, yamada-shota@aist go jp

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2018/1000

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