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Optimizing Obfuscation: Avoiding Barrington’s Theorem
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BibTeX
@MISC{Ananth_optimizingobfuscation:,
author = {Prabhanjan Ananth and Divya Gupta and Yuval Ishai and Amit Sahai},
title = {Optimizing Obfuscation: Avoiding Barrington’s Theorem},
year = {}
}
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Abstract
In this work, we seek to optimize the efficiency of secure general-purpose obfuscation schemes. We focus on the problem of optimizing the obfuscation of general Boolean formulas – this cor-responds to optimizing the “core obfuscator ” from the work of Garg, Gentry, Halevi, Raykova, Sahai, and Waters (FOCS 2013), and all subsequent works constructing general-purpose ob-fuscators. This core obfuscator builds upon approximate multilinear maps, where efficiency in proposed instantiations is closely tied to the maximum number of “levels ” of multilinearity required. The most efficient previous construction of a core obfuscator, due to Barak, Garg, Kalai, Paneth, and Sahai (Eurocrypt 2014), required the maximum number of levels of multilinearity to be Θ(`s3.64), where s is the size of the Boolean formula to be obfuscated, and ` is the number of input bits to the formula. In contrast, our construction only requires the maximum number of levels of multilinearity to be Θ(`s). This results in significant improvements in both the total size of the obfuscation, as well as the running time of evaluating an obfuscated formula. Our efficiency improvement is obtained by generalizing the class of branching programs that
Keyphrases
avoiding barrington core obfuscator maximum number significant improvement input bit boolean formula obfuscated formula secure general-purpose obfuscation scheme general-purpose ob-fuscators total size general boolean formula proposed instantiation running time approximate multilinear map efficient previous construction subsequent work efficiency improvement
