Indistinguishability Obfuscation of Circuits and its Application in Security

Under discussion in the paper is an $i\mathcal{O}$ (indistinguishability obfuscator) for circuits in Nick's Class. The obfuscator is constructed by encoding the Branching Program given by Barrington's theorem using Multilinear Jigsaw Puzzle framework. We will show under various indistinguishability hardness assumptions, the constructed obfuscator is an $i\mathcal{O}$ for Nick's Class. Using Fully Homomorphic Encryption, we will amplify the result and construct an $i\mathcal{O}$ for $\textbf{P}/poly$, which are circuits of polynomial size. Discussion on $i\mathcal{O}$ and Functional Encryption is also included in this paper.