Limits on the Locality of Pseudorandom Generators and Applications to Indistinguishability Obfuscation

Lin and Tessaro (ePrint 2017) recently proposed indistinguishability obfuscation (IO) and functional encryption (FE) candidates and proved their security based on two assumptions: a standard assumption on bilinear maps and a non-standard assumption on “Goldreich-like” pseudorandom generators. In a nutshell, their second assumption requires the existence of pseudorandom generators G : [q] → {0, 1} for some poly(n)-size alphabet q, each of whose output bits depend on at most two in put alphabet symbols, and which achieve sufficiently large stretch. We show polynomial-time attacks against such generators, invalidating the security of the IO and FE candidates. Our attack uses tools from the literature on two-source extractors (Chor and Goldreich, SICOMP 1988) and efficient refutation of random 2-XOR instances (Charikar and Wirth, FOCS 2004). ∗Supported by an Akamai Presidential Fellowship and the grants of the second author. †E-mail: [email protected]. Research supported in part by NSF Grants CNS-1350619 and CNS-1414119, Alfred P. Sloan Research Fellowship, Microsoft Faculty Fellowship, the NEC Corporation, a Steven and Renee Finn Career Development Chair from MIT. This work was also sponsored in part by the Defense Advanced Research Projects Agency (DARPA) and the U.S. Army Research Office under contracts W911NF-15-C-0226 and W911NF-15-C-0236.