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.
CITATION STYLE
Attrapadung, N., Matsuda, T., Nishimaki, R., Yamada, S., & Yamakawa, T. (2019). Adaptively Single-Key Secure Constrained PRFs for $$\mathrm {NC}^1$$. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11443 LNCS, pp. 223–253). Springer Verlag. https://doi.org/10.1007/978-3-030-17259-6_8
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