New Techniques for Obfuscating Conjunctions

A conjunction is a function \(f(x_1,\dots ,x_n) = \bigwedge _{i \in S} l_i\) where \(S \subseteq [n]\) and each \(l_i\) is \(x_i\) or \(\lnot x_i\). Bishop et al. (CRYPTO 2018) recently proposed obfuscating conjunctions by embedding them in the error positions of a noisy Reed-Solomon codeword and placing the codeword in a group exponent. They prove distributional virtual black box (VBB) security in the generic group model for random conjunctions where \(|S| \ge 0.226n\). While conjunction obfuscation is known from LWE [31, 47], these constructions rely on substantial technical machinery.