Indistinguishability Obfuscation of Circuits and its Application in Security

TL;DR

This paper constructs an indistinguishability obfuscator for circuits in Nick's Class using multilinear jigsaw puzzles, and extends it to polynomial-size circuits with fully homomorphic encryption, discussing related cryptographic concepts.

Contribution

It introduces a new construction of an $i\mathcal{O}$ for Nick's Class and extends it to $P/poly$ circuits using FHE, advancing obfuscation techniques.

Findings

Constructed an $i\mathcal{O}$ for Nick's Class based on Barrington's theorem.

Amplified the obfuscator to polynomial-size circuits using Fully Homomorphic Encryption.

Discussed the relationship between $i\mathcal{O}$ and Functional Encryption.

Abstract

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.