# On the Non-Existence of Blockwise 2-Local PRGs with Applications to Indistinguishability Obfuscation

 dc.date.accessioned 2017-04-06T23:00:10Z dc.date.accessioned 2018-11-26T22:27:42Z dc.date.available 2017-04-06T23:00:10Z dc.date.available 2018-11-26T22:27:42Z dc.date.issued 2017-04-06 dc.identifier.uri http://hdl.handle.net/1721.1/107928 dc.identifier.uri http://repository.aust.edu.ng/xmlui/handle/1721.1/107928 dc.description.abstract Lin and Tessaro (Eprint 2017/250) recently proposed indistinguishability obfuscation and functional encryption candidates and proved their security based on a standard assumption on bilinear maps and a non-standard assumption on Goldreich-like'' pseudorandom generators (PRG). In a nutshell, they require the existence of pseudo-random generators $G:\Sigma^n \to \{0,1\}^m$ for some $\mathsf{poly}(n)$-size alphabet $\Sigma$ where each output bit depends on at most two input alphabet symbols, and which achieve sufficiently large stretch. We show a polynomial-time attack against such generators. Our attack uses tools from the literature on two-source extractors (Chor and Goldreich, SICOMP 1988) and efficient refutation of 2-CSPs over large alphabets (Allen, O'Donnell and Witmer, FOCS 2015). Finally, we propose new ways to instantiate the Lin-Tessaro construction that do not immediately fall to our attacks. While we cannot say with any confidence that these modifications are secure, they certainly deserve further cryptanalysis. en_US dc.format.extent 12 p. en_US dc.subject Indistinguishability Obfuscation en_US dc.title On the Non-Existence of Blockwise 2-Local PRGs with Applications to Indistinguishability Obfuscation en_US
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