[sterlind]

Not even theoretically possible, as far as I can tell. If iO is protecting your decryption key, then any indistinguishable circuit would also include your decryption key in some form.

I'm having trouble thinking of cases where iO gives you any actual guarantees that matter, because of this property.

[aruss]

If you're interested, check out the paper called "How to Use Indistinguishability Obfuscation" by Sahai and Waters. They were able to prove some very surprising things -- including how to hide a private key by way of iO.