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]n → {0,1}m 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).
CITATION STYLE
Lombardi, A., & Vaikuntanathan, V. (2017). Limits on the Locality of Pseudorandom Generators and Applications to Indistinguishability Obfuscation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10677 LNCS, pp. 119–137). Springer Verlag. https://doi.org/10.1007/978-3-319-70500-2_5
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