Oblivious Transfer from Quantum One-way Functions
Yilun Wang

Abstract:
Secure Multi-party Computation (MPC), which allows multiple parties to jointly compute a function over their inputs while keeping the inputs private, is one of the important research directions in cryptography, and plays a vital role in fields like auctions and electronic votes.
Oblivious Transfer (OT) protocols are sufficient to construct MPC protocols. We provide a construction turning any (classical) Zero-Knowledge (ZK) protocol into a composable quantum Oblivious Transfer (OT) protocol, using weaker assumptions compared to previous works while keeping a protocol optimal in communication.
In particular, this construction only requires collision-resistant quantum one-way functions, instead of collision-resistant hiding hash functions, to build a 2-message quantum OT protocol in the random oracle model.
Internally, we rely on a quantum version of the Goldreich-Levin theorem that we generalize to arbitrary length-preserving one-way functions instead of one-way permutations. This theorem provides a way to generate a quantum hard-predicate that is used in the protocol to hide one bit of information without relying on the hiding property.