will describe an obfuscator for all circuits based on graded encoding schemes (a generalization of multilinear maps). This construction inspired by the previous work of Garg et al. (FOCS 13) and by our previous obfuscators for more restricted function classes. I will show that the security of this obfuscator, either as an indistinguishability obfuscator (iO) or even as a virtual black box obfuscator (VBB), can be proven in a generic model. The VBB proof will require an additional complexity theoretic (worst case) hardness assumption that is related to the exponential time hypothesis. One way to interpret this model is a setting where the adversary is only allowed "algebraic" attacks on the underlying graded encoding scheme.
Joint work with Guy Rothblum.