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In a recent celebrated breakthrough, Garg et al. (FOCS 2013) gave the first candidate for so-called indistinguishability obfuscation (iO) thereby reviving the interest in obfuscation for a general purpose. Since then, iO has been used to advance numerous sub-areas of cryptography. While indistinguishability obfuscation is a general purpose obfuscation scheme, several obfuscators for specific functionalities have been considered. In particular, special attention has been given to the obfuscation of so-called point functions that return zero everywhere, except for a single point x. A strong variant is point obfuscation with auxiliary input (AIPO), which allows an adversary to learn some non-trivial auxiliary information about the obfuscated point x (Goldwasser, Tauman-Kalai; FOCS, 2005).

Indistinguishability Obfuscation versus Multi-bit Point Obfuscation with Auxiliary Input