2019 | OriginalPaper | Chapter
New Techniques for Obfuscating Conjunctions
Authors : James Bartusek, Tancrède Lepoint, Fermi Ma, Mark Zhandry
Published in: Advances in Cryptology – EUROCRYPT 2019
Publisher: Springer International Publishing
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Abstract
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We abstract the Bishop et al. scheme to obtain an equivalent yet more efficient “dual” scheme that can handle conjunctions over exponential size alphabets. This scheme admits a straightforward proof of generic group security, which we combine with a novel combinatorial argument to obtain distributional VBB security for |S| of any size.
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If we replace the Reed-Solomon code with a random binary linear code, we can prove security from standard LPN and avoid encoding in a group. This addresses an open problem posed by Bishop et al. to prove security of this simple approach in the standard model.
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We give a new construction that achieves information theoretic distributional VBB security and weak functionality preservation for \(|S| \ge n - n^\delta \) and \(\delta < 1\). Assuming discrete log and \(\delta < 1/2\), we satisfy a stronger notion of functionality preservation for computationally bounded adversaries while still achieving information theoretic security.