Candidate Indistinguishability Obfuscation and Functional Encryption for All Circuits

Abstract

In this work, we study indistinguishability obfuscation and functional encryption for general circuits: Indistinguishability obfuscation requires that given any two equivalent circuits $C_0$ and $C_1$ of similar size, the obfuscations of $C_0$ and $C_1$ should be computationally indistinguishable. In functional encryption, ciphertexts encrypt inputs $x$ and keys are issued for circuits $C$. Using the key $\mathrm{SK}_C$ to decrypt a ciphertext $\mathrm{CT}_x={\sf Enc}(x)$ yields the value $C(x)$ but does not reveal anything else about $x$. Furthermore, no collusion of secret key holders should be able to learn anything more than the union of what they can each learn individually. We give constructions for indistinguishability obfuscation and functional encryption that supports all polynomial-size circuits. We accomplish this goal in three steps: (1) We describe a candidate construction for indistinguishability obfuscation for $\mathbf{NC}^1$ circuits. The security of this construction is based on a new al...