On Perfect Correctness in (Lockable) Obfuscation.
Rishab Goyal, Venkata Koppula, Satyanarayana Vusirikala, Brent R. Waters · IACR Cryptology ePrint Archive · 2019
In a lockable obfuscation scheme [28, 39] a party takes as input a program P, a lock value \(\alpha \), a message \(\mathsf {msg}\) and produces an obfuscated program \(\tilde{P}\). The obfuscated program can be evaluated on an input x to learn the message \(\mathsf {msg}\) if \(P(x)= \alpha \). The security of such schemes states that if \(\alpha \) is randomly chosen (independent of P and \(\mathsf {msg}\)), then one cannot distinguish an obfuscation of P from a “dummy” obfuscation. Existing constructions of lockable obfuscation achieve provable security under the Learning with Errors assumption. One limitation of these constructions is that they achieve only statistical correctness and allow for a possible one sided error where the obfuscated program could output the \(\mathsf {msg}\) on some value x where \(P(x) e \alpha \).