We will discuss how quantum information can be used to relax assumptions required for cryptography, and specifically the core cryptographic task of secure multiparty computation (MPC). This allows a set of mutually distrustful parties to jointly compute a function of their private inputs, while only revealing the output and hiding all other private information. In contrast to the classical setting, quantum communication can be used to realize general-purpose MPC based on the weak (and therefore, more reliable) cryptographic assumption that one-way functions exist. To obtain this result, it suffices to focus on oblivious transfer (OT), which is complete for MPC.
We will discuss the history of this line of research beginning with the seminal work of Crepeau and Kilian, all the way to recent ideas showing how one-way functions (and perhaps even weaker assumptions) imply OT, and therefore MPC, in a quantum world.
"Founding Cryptography on Oblivious Transer." https://dl.acm.org/doi/pdf/10.1145/62212.62215
"Achieving Oblivious Transfer using Weakened Security Assumptions." https://ieeexplore.ieee.org/document/21920
"Sampling in a Quantum Population, and Applications." https://arxiv.org/pdf/0907.4246.pdf
"One Way Functions Imply Secure Computation in a Quantum World." https://arxiv.org/abs/2011.13486
"Oblivious Transfer is in MiniQCrypt." https://arxiv.org/abs/2011.14980
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