(Fully) Homomorphic Encryption is necessary for this. One of the paper's authors (Craig Gentry) is also the creator of FHE. To quote the paper:
>Using indistinguishability obfuscator for NC^1 together with any (leveled) fully homomorphic encryption (FHE) scheme with decryption in NC^1 (e.g. [Gen09b, BV11, BGV12, Bra12, GSW13])
Paper: http://eprint.iacr.org/2013/451.pdf
I have not read through the paper (yet, I plan to).
>Using indistinguishability obfuscator for NC^1 together with any (leveled) fully homomorphic encryption (FHE) scheme with decryption in NC^1 (e.g. [Gen09b, BV11, BGV12, Bra12, GSW13])
I have not read through the paper (yet, I plan to).