Structure-Preserving Compilers from New Notions of Obfuscations

Matteo Campanelli, Danilo Francati, Claudio Orlandi

Abstract: The dream of software obfuscation is to take programs, as they are, and then generically compile them into obfuscated versions that hide their secret inner workings. In this work we investigate notions of obfuscations weaker than virtual black-box ( $$\textsf{VBB} $$ ) but which still allow obfuscating cryptographic primitives preserving their original functionalities as much as possible. In particular we propose two new notions of obfuscations, which we call oracle-differing-input obfuscation ( $$\textsf{odiO} $$ ) and oracle-indistinguishability obfuscation ( $$\textsf{oiO} $$ ). In a nutshell, $$\textsf{odiO} $$ is a natural strengthening of differing-input obfuscation ( $$\textsf{diO} $$ ) and allows obfuscating programs for which it is hard to find a differing-input when given only oracle access to the programs. An $$\textsf{oiO} $$ obfuscator allows to obfuscate programs that are hard to distinguish when treated as oracles. We then show applications of these notions, as well as positive and negative results around them. A few highlights include: