On Statistically Secure Obfuscation with Approximate Correctness

Goldwasser and Rothblum (TCC ’07) prove that statistical indistinguishability obfuscation (iO) cannot exist if the obfuscator must maintain perfect correctness (under a widely believed complexity theoretic assumption: NP ⊆ SZK ⊆ AM ∩ coAM). However, for many applications of iO, such as constructing public-key encryption from one-way functions (one of the main open problems in theoretical cryptography), approximate correctness is sufficient. It had been unknown thus far whether statistical approximate iO (saiO) can exist. We show that saiO does not exist, even for a minimal correctness requirement, if NP ⊆ AM ∩ coAM, and if one-way functions exist. A simple complementary observation shows that if one-way functions do not exist, then average-case saiO exists. Technically, previous approaches utilized the behavior of the obfuscator on evasive functions, for which saiO always exists. We overcome this barrier by using a PRF as a “baseline” for the obfuscated program. We bro...

• Type: Journal
• Year: 2016
• Where: IACR
• Authors: Zvika Brakerski, Christina Brzuska, Nils Fleischhacker
• Keywords: Biometrics, IACR 2016