Abstract

We consider indistinguishability obfuscation (iO) for multi-output circuits of size s, where s is the number of AND/OR/NOT gates in C. Under the worst-case assumption that NP not in BPP, we establish that there is no efficient indistinguishability obfuscation scheme that outputs circuits of size s+ o(s/log s). In other words, to be secure, an efficient iO scheme must incur an s/log s additive overhead in the size of the obfuscated circuit.

The proof of our main result builds on a connection between obfuscation and meta-complexity, and on the NP-hardness of circuit minimization for multi-output circuits established by Loff, Ilango, and Oliveira [ILO20], together with other techniques from cryptography and complexity theory.

Based on a joint work with Zhenjian Lu, Igor C. Oliveira and Rafael Pass.