Obfuscation without Multilinear Maps

Known methods for obfuscating a circuit need to represent the circuit as a branching program and then use a multilinear map to encrypt the branching program. Multilinear maps are, however, too inefficient for encrypting the branching program. We found a dynamic encoding method which effectively singles out different inputs in the context of the matrix randomization technique of Kilian and Gentry et al., so that multilinear maps are no longer needed. To make the method work, we need the branching programs to be regular. For such branching programs, we also give most efficient constructions for NC1 circuits. This results in a much more efficient core obfuscator for NC1 circuits.