Secure Two-Party Computation in a Quantum World

Secure multi-party computation has been extensively studied in the past years and has reached a level that is considered practical for several applications. The techniques developed thus far have been steadily optimized for performance and were shown to be secure in the classical setting, but are not known to be secure against quantum adversaries. In this work, we start to pave the way for secure two-party computation in a quantum world where the adversary has access to a quantum computer. We show that post-quantum secure two-party computation has comparable efficiency to their classical counterparts. For this, we develop a lattice-based OT protocol which we use to implement a post-quantum secure variant of Yao's famous garbled circuits (GC) protocol (FOCS'82). Along with the OT protocol, we show that the oblivious transfer extension protocol of Ishai et al. (CRYPTO'03), which allows running many OTs using mainly symmetric cryptography, is post-quantum secure. To support these results, we prove that Yao's GC protocol achieves post-quantum security if the underlying building blocks do.