Obfuscation from Polynomial Hardness: Beyond Decomposable Obfuscation

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.