On White-box Cryptography and Obfuscation

We study the relationship between obfuscation and white-box cryptography. We capture the requirements of any white-box primitive using a White-Box Property (WBP) and give some negative/positive results. Loosely speaking, the WBP is defined for some scheme and a security notion (we call the pair a specification), and implies that w.r.t. the specification, an obfuscation does not leak any “useful” information, even though it may leak some “useless” non-black-box information. Our main result is a negative one for most interesting programs, an obfuscation (under any definition) cannot satisfy the WBP for every specification in which the program may be present. To do this, we define a Universal White-Box Property (UWBP), which if satisfied, would imply that under whatever specification we conceive, the WBP is satisfied. We then show that for every non-approximately-learnable family, there exist (contrived) specifications for which the WBP (and thus, the UWBP) fails. On the positive side, we show that there exists an obfuscator for a non-approximately-learnable family that achieves the WBP for a certain specification. Furthermore, there exists an obfuscator for a non-learnable (but approximately-learnable) family that achieves the UWBP. Our results can also be viewed as formalizing the distinction between “useful” and “useless” non-black-box information.