On the Implausibility of Differing-Inputs Obfuscation and Extractable Witness Encryption with Auxiliary Input

The notion of differing-inputs obfuscation (diO) was introduced by Barak et al. (CRYPTO 2001). It guarantees that, for any two circuits C0, C1, if it is difficult to come up with an input x on which C0(x) ≠ C1(x), then it should also be difficult to distinguish the obfuscation of C0 from that of C1. This is a strengthening of indistinguishability obfuscation, where the above is only guaranteed for circuits that agree on all inputs: C0(x) = C1(x) for all x. Two recent works of Ananth et al. (ePrint 2013) and Boyle et al. (TCC 2014) study the notion of diO in the setting where the attacker is also given some auxiliary information related to the circuits, showing that this notion leads to many interesting applications.

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