Impossibility of VBB Obfuscation with Ideal Constant-Degree Graded Encodings

@misc{PS15a,
 author = {Rafael Pass and abhi shelat},
 title = {Impossibility of VBB Obfuscation with Ideal Constant-Degree Graded Encodings},
 booktitle = {To Appear, TCC 2016, and eprint.iacr.org/2015/383},
 year = {2015},
}

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A celebrated result by Barak et al (JACM’12) shows the imposibility of general-purpose virtual black-box (VBB) obfuscation in the plain model. A recent work by Canetti, Kalai, and Paneth (TCC’15) extends this result also to the random oracle model (assuming trapdoor permutations).

In contrast, Brakerski-Rothblum (TCC’15) and Barak et al (EuroCrypt’14) show that in idealized graded encoding models, general-purpose VBB obfuscation indeed is possible; these construction require graded encoding schemes that enable evaluating high-degree (polynomial in size of the circuit to be obfuscated) polynomials on encodings.

We show a complementary impossibility of general-purpose VBB obfuscation in idealized graded encoding models that enable only evaluation of constant-degree polynomials (assuming trapdoor permutations).