Obfuscation of Hyperplane Membership

Abstract

Previous work on program obfuscation gives strong negative results for general-purpose obfuscators, and positive results for obfuscating simple functions such as equality testing (point functions). In this work, we construct an obfuscator for a more complex algebraic functionality: testing for membership in a hyperplane (of constant dimension). We prove the security of the obfuscator under a new strong variant of the Decisional Diffie-Hellman assumption. Finally, we show a cryptographic application of the new obfuscator to digital signatures.