Obfuscating Branching Programs Using Black-Box Pseudo-Free Groups

We show that the class of polynomial-size branching programs can be obfuscated according to a virtual black-box notion akin to that of Barak et.al., in an idealized black-box group model over pseudo-free groups. This class is known to lie between NC 1 and P and includes most interesting cryptographic algorithms. The construction is rather simple and is based on Kilian’s randomization technique for Barrington’s branching programs. The black-box group model over pseudo-free groups is a strong idealization. In particular, in a pseudo-free group, the group operation can be eciently performed, while nding surprising relations between group elements is intractable. A black-box representation of the group provides an ideal interface which permits prescribed group operations, and nothing else. Still, the algebraic structure and security requirements appear natural and potentially realizable. They are also unrelated to the specic