Obfuscating Point Functions with Multibit Output

We study obfuscation of point functions with multibit output and other related functions. A point function with multibit output returns a string on a single input point and zero everywhere else. We provide a construction that obfuscates these functions. The construction is generic in the sense that it can use any perfectly one-way (POW) function or obfuscator for point functions. Analyzing this construction reveals gaps in the definition of obfuscation, specifically, that it does not guarantee security even under self-composition, a property needed in our analysis. Thus, we use obfuscation secure under composition. In particular, we show that composable obfuscation of multibit point functions exists if and only if composable obfuscation of point functions exists. Moreover, we show that this construction is secure based on statistically indistinguishable POW functions. However, if we relax the assumption to computational indistinguishability, then the construction satisfies a weaker notion of obfuscation. Finally, the same technique can be used to obfuscate set-membership predicates and functions, for polynomial-size sets.