Every known construction of general indistinguishability obfuscation ($\mathsf{i}\mathcal{O}$) is either based on a family of exponentially many
assumptions, or is based on a single assumption — e.g.~functional encryption ($\mathsf{FE}$) — using a reduction that incurs an exponential loss in security. This seems to be an inherent limitation if we insist on providing indistinguishability for any pair of functionally equivalent circuits. Recently, Liu and Zhandry (TCC 2017) introduced the notion of decomposable $\mathsf{i}\mathcal{O}$ ($\mathsf{d}\mathcal{O}$), which provides indistinguishability for a restricted class of functionally equivalent circuit pairs, and, as the authors show, can be constructed from polynomially secure $\mathsf{FE}$. In this paper we propose a new notion of obfuscation, termed $\mathsf{radi}\mathcal{O}$ (repeated-subcircuit and decomposable obfuscation), which allows us to obfuscate a strictly larger class of circuit pairs using a polynomial reduction to $\mathsf{FE}$. Our notion builds on the equivalence criterion of Liu and Zhandry, combining it with a new incomparable criterion to obtain a strictly larger class.

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