Impossibility of VBB Obfuscation with Ideal Constant-Degree Graded Encodings

A celebrated result by Barak et al (JACM’12) shows the impossibility 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, generalpurpose VBB obfuscation indeed is possible; these construction require graded encoding schemes that enable evaluating high-degree (polynomial in the 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). ∗Cornell University, [email protected]. Work supported in part by a Alfred P. Sloan Fellowship, Microsoft New Faculty Fellowship, NSF Award CNS-1217821, NSF CAREER Award CCF-0746990, NSF Award CCF-1214844, AFOSR YIP Award FA9550-10-10093, and DARPA and AFRL under contract FA8750-11-2-0211. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Defense Advanced Research Projects Agency or the US Government. †U. of Virginia [email protected]. Work performed while visiting Cornell Tech, and supported by NSF CAREER Award 0845811, NSF TC Award 1111781, NSF TC Award 0939718, DARPA and AFRL under contract FA8750-11-C-0080, Microsoft New Faculty Fellowship, SAIC Scholars Research Award, and Google Research Award.