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:

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.

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.

Finally, we show how to use indistinguishability obfuscation for circuits, public-key encryption, and non-interactive zero knowledge to achieve functional encryption for all circuits. The functional encryption scheme we construct also enjoys succinct ciphertexts, which enables several other applications.

joint work with Sanjam Garg, Craig Gentry, Shai Halevi, Amit Sahai, Brent Waters

Speaker Details

Mariana Raykova is a researcher in cryptography at SRI International. She received her PhD in 2012 from Columbia University advised by Tal Malkin and Steve Bellovin. Her PhD work focused on secure computation and bringing cryptographic constructions closer to practical uses. She spent a year as a postdoc in the cryptography group at IBM Research Watson, where she worked on obfuscation, functional encryption and verifiable computation. She did three summer internships during her PhD at MSR Redmond working in the cryptography and security groups.

Date:
Speakers:
Mariana Raykova
Affiliation:
SRI International

Series: Microsoft Research Talks