Evaluating Encrypted Boolean Functions on Encrypted Bits: Secure Decision-making on the Black side

We present a novel approach for secure evaluation of encrypted Boolean functions on encrypted bits. Building upon Barrington’s work to transform circuits to group programs and the Feige-Kilian-Naor cryptographic protocol, our novel Fixed Structure Group Program construction for secure evaluation eliminates the need for an expensive Universal Circuit to hide the function. Elements on the Black side weave together and multiply two coordinated streams of random sequences of elements from an unsolvable group; the Boolean decision is recovered while preserving the confidentiality of the decision function and the input bits. The operation is fast and can be further sped up using parallel computation. Our approach can handle expressions with NC 1 complexity, which is the class of Acyclic Boolean Circuits with polynomial width and logarithmic depth in the size of the input. This efficiently parallelizable class includes nonmonotone Boolean expressions of equality, inequality/range, Hamming distance, Boolean matrix multiplication, and kof-m threshold matching operations. The combined benefits of scaling and expressivity of our approach enables secure decision-making on the Black side. Envisioned applications include confidential publish/subscribe systems (with empirically validated performance), secure content-oriented internetworks, confidential forwarding and firewalling rules, and cross-domain guards.