A Simple Obfuscation Scheme For Pattern-Matching With Wildcards

We give a simple and efficient method for obfuscating pattern matching with wildcards. In other words, we construct a way to check an input against a secret pattern, which is described in terms of prescribed values interspersed with unconstrained "wildcard" slots. As long as the support of the pattern is sufficiently sparse and the pattern itself is chosen from an appropriate distribution, we prove that a polynomial-time adversary cannot find a matching input, except with negligible probability. We rely upon the generic group heuristic (in a regular group, with no multilinearity). Previous work [9,10,32] provided less efficient constructions based on multilinear maps or LWE.