Obfuscating Finite Automata

We construct a virtual black box and perfect circuit-hiding obfuscator for evasive deterministic finite automata using a matrix encoding scheme with a limited zero-testing algorithm. We construct the matrix encoding scheme by extending an existing matrix fully homomorphic encryption scheme. Using obfuscated deterministic finite automata we can for example evaluate secret regular expressions or disjunctive normal forms on public inputs. In particular, the possibility of evaluating regular expressions solves the open problem of obfuscated substring matching.