On the Non-Existence of Blockwise 2-Local PRGs with Applications to Indistinguishability Obfuscation
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MIT-CSAIL-TR-2017-005.pdf
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Author(s)
Lombardi, Alex
Vaikuntanathan, Vinod
Advisor(s)
Vinod Vaikuntanathan
Date Issued
April 6, 2017
Series/Report no.
MIT-CSAIL-TR-2017-005
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.
Subjects
Indistinguishability Obfuscation
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