Candidate Indistinguishability Obfuscation and Functional Encryption for All Circuits

In this work, we study indistinguishability obfuscation and functional encryption for general circuits: Indistinguishability obfuscation requires that given any two equivalent circuits C₀ and C₁ of similar size, the obfuscations of C₀ and C₁ should be computationally indistinguishable. In functional encryption, ciphertexts encrypt inputs x and keys are issued for circuits C. Using the key SKC to decrypt a ciphertext CTₓ= 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 NC¹ circuits. The security of this construction is based on a new algebraic hardness assumption. The candidate and assumption use a simplified variant of multilinear maps, which we call multilinear jigsaw puzzles. (2) We show how to use indistinguishability obfuscation for NC¹ together with fully homomorphic encryption (with decryption in NC¹) to achieve indistinguishability obfuscation for all circuits. (3) Finally, we show how to use indistinguishability obfuscation for circuits, public-key encryption, and noninteractive zero knowledge to achieve functional encryption for all circuits. The functional encryption scheme we construct also enjoys succinct ciphertexts, which enables several other applications.