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If I’m not mistaken classical OT is not regarded quanum-safe. However I’ve been reading (not really understanding) some papers [1,2] and some reviews[3] on quantum OT and/or post-quantum OT, it seems to be possible.

I do have an engineering background, so that’s the reason why I don’t get quantum cryptography papers.

Can you please explain briefly in layman (engineer) terms if and how post-quantum OT is possible?

[1] https://www.computer.org/csdl/proceedings/phycmp/1994/6715/00/00363696.pdf

[2] http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.650.385&rep=rep1&type=pdf

[3] https://www.quantiki.org/wiki/oblivious-transfer

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    $\begingroup$ Do you just want an OT protocol secure against a quantum attacker? If so, there are post-quantum secure OT protocols based on lattices or coding theory assumptions, which don't require any quantum cryptography. $\endgroup$ – pscholl Sep 13 '18 at 9:34
  • $\begingroup$ @pscholl Yes, I’m very much interested in post-quantum secure OT protocols. The only reason I mentioned quantum OT is, those were the ones I came across. Any OT protocol secure against a quantum attacker is more than good enough for what I’m trying to build. If you know of a simple and practical one, can you point me towards one (1-2 or even something like Rabin OT is simply good enough for my use-case) $\endgroup$ – zetaprime Sep 13 '18 at 9:56
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    $\begingroup$ Also isogeny based ones: eprint.iacr.org/2018/459 $\endgroup$ – Luca De Feo Sep 13 '18 at 10:03
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Post-quantum oblivious transfer protocols are possible. If you base the security of the OT in a post-quantum assumption, this should give you an OT conjectured to be robust to quantum attackers. Besides the already mentioned OT based on supersingular isogeny (in comments), I can give you some other examples:

Code-based: https://eprint.iacr.org/2008/138.pdf , https://ieeexplore.ieee.org/document/6089575

Lattice-based: https://eprint.iacr.org/2018/530

There are also some constructions for OT ,secure in the Universally Composable framework and based on post-quantum assumptions, such as

https://link.springer.com/chapter/10.1007/978-3-319-12280-9_10

based on the LPN assumption, and the ones that can be instantiated using the frameworks of:

https://eprint.iacr.org/2007/348.pdf

and

https://eprint.iacr.org/2017/993.pdf

using post-quantum encryption schemes.

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