Public-Coin Differing-Inputs Obfuscator for Hiding-Input Point Function with Multi-bit Output and Its Applications

Paper in proceeding, 2019

Differing-inputs obfuscation (diO), first introduced by Barak et al. (CRYPTO 2001) and then revisited by Ananth et al. (ePrint 2013) and Boyle et al. (TCC 2014), is a natural extension of indistinguishability obfuscation (iO), which captures a security notion that the obfuscations of two efficiently generated programs (Formula Presented) and (Formula Presented) are indistinguishable if it is hard for an adversary to find an input x such that (Formula Presented), even in the presence of auxiliary information aux that is generated together with (Formula Presented) and (Formula Presented). A variant notion of diO, called public-coin diO, introduced by Ishai, Pandey and Sahai (TCC 2015) relaxes the original definition of diO by requiring that only the actual random coins that were used to sample programs (Formula Presented) and (Formula Presented) can be used as the auxiliary input. Public-coin diO is indeed of great interest, since it not only allows to evade the implausible results of diO, but also yields several useful applications. However, as far as we know, there was no approach known to build a public-coin differing-input obfuscator neither for general-purpose programs/circuits such as NC(Formula Presented) circuits nor for special-purpose function such as some variant of point function. In this paper, we propose a public-coin differing-inputs obfuscator for a class of function, namely hiding-input point function with multi-bit output (MB-HIPF). We show that the existence of public-coin diO for MB-HIPF can be implied under the existence of auxiliary input point obfuscation for unpredictable distrins (AIPO) which can be instantiated under different assumptions (TCC 2012), and the conjecture of the existence of a special-purpose obfuscation for MB-HIPF, which has been considered as a falsifiable assumption (CRYPTO 2014). Besides, we show the applications of public-coin diO for MB-HIPF. We emphasize that even though our result is based on the special-purpose obfuscation conjecture, it at least provides a different mindset on constructing public-coin diO from more concrete building blocks, i.e., a special-purpose obfuscation for MB-HIPF and AIPO. Then we can turn to investigating these specific primitives with a more focused mindset.