Quantum Oblivious Transfer

Corresponds to Chapters 12.3–14. Oblivious transfer is a two-party primitive strictly more powerful than it looks: a sender holds two messages $m_0, m_1$, a receiver picks a bit $b$, and the protocol must ensure the receiver learns $m_b$ and nothing about $m_{1-b}$, while the sender learns nothing about $b$ — a primitive from which general secure multi-party computation can be built (see secret-sharing-multi-party-and-computational-differential-privacy for the broader MPC context). Classically, OT needs a computational assumption; covers the security definitions against a malicious sender and against a malicious receiver separately, and commitment schemes (binding + hiding) as a building block several OT constructions need. The quantum attempt at information-theoretically-secure OT uses no-cloning-style arguments instead of computational hardness, with a proof-of-measurement technique for forcing a party to commit to having actually measured a qubit (rather than keeping it coherent to cheat later), and a security analysis specifically against a malicious receiver (“Bob”).

Outline (TODO — flesh out each)

• Oblivious transfer — definition
• Security against malicious senders
• Security against malicious receivers
• Commitment schemes
• Quantum information-theoretically-secure OT — the attempt
• Proof of measurement
• Security against malicious Bob