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I'm looking for a textbook or article that spells out the details of Kilian's paper on the completeness of oblivious transfer for secure two-party function evaluation (2PC). Kilian's paper is in the form of an extended abstract which doesn't include many of the details. Moreover, there have been many development in the 2PC theory since Kilian's seminal work, such as the universal composability framework of Canetti. An ideal reference would be one that gives a full proof of the completeness of OT in this framework.

I have read Oded Goldreich's book chapter on 2PC which uses commitments and ZKProofs to compile a semi-honest protocol into a maliciously secure protocol. However, I'm mostly interested in the OT-based approach of Kilian.

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  • $\begingroup$ Are you more interested in an exposition of Kilian's protocol, or any protocol establishing the completeness of OT? Also, do you care about information-theoretic security? Kilian's result is an information-theoretic protocol for any 2PC from OT. If you are OK with computational assumptions, then variants of Yao's protocol can give you any 2PC from OT. $\endgroup$
    – Mikero
    Jul 27, 2023 at 23:37
  • $\begingroup$ I'm interested in the information theoretic setting (where OT is the only assumption). References that use other techniques than Kilian's to establish the completeness of OT in an info theoretic setting are also welcome. $\endgroup$
    – lamontap
    Jul 28, 2023 at 14:06

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The paper that comes to mind is:

Founding Cryptography on Oblivious Transfer – Efficiently: Yuval Ishai, Manoj Prabhakaran, Amit Sahai

You can tell by the title that it is following in Kilian's footsteps. The protocol is a bit more complicated, since it uses MPC-in-the-head techniques (so if you want to understand the complete protocol from scratch, you first have to understand an actively secure protocol in the honest majority setting and a passively secure protocol in the dishonest majority setting). But the paper gives rather full details. In other references, you'll see this construction referred to as "the IPS compiler."

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  • $\begingroup$ This is very close to what I was looking for. Appendix B especially for the two-party case. Thanks! $\endgroup$
    – lamontap
    Jul 31, 2023 at 19:48

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