Virtual Black-Box Obfuscation for All Circuits via Generic Graded Encoding

We present a new general-purpose obfuscator for all polynomial size circuits. The obfuscator uses graded encoding schemes, a generalization of multilinear maps. We prove that the obfuscator exposes no more information than the program’s black-box functionality, and achieves virtual black-box security, in the generic graded encoded scheme model. This proof is under the Bounded Speedup Hypothesis (BSH, a plausible worst-case complexity-theoretic assumption related to the Exponential Time Hypothesis), in addition to standard cryptographic assumptions. We also prove that it satisfies the notion of indistinguishability obfuscation without without relying on BSH (in the same generic model and under standard cryptographic assumptions).

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