Are there any optimised implementations of the Supersingular Isogeny Key Exchange by Defeo, Jao, and Plut. It seems like this would be a great drop-in replacement for Diffie-Hellman in both OpenSSL and GPG. I'm wondering if that code is available or if someone is working on it.
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The inventors of the Supersingular Isogeny Key Exchange, Defeo, Jao and Plut have posted some code on GITHUB at:
There is also a paper on implementation of this key exchange by some people from the University of Waterloo. Their paper is "Efficient Implementations of A Quantum-Resistant Key-Exchange Protocol on Embedded systems" and can be found:
I would also like to note that while Lattice Based Cryptography (as suggested by the other answer) is more efficient than the Isogeny based key exchange it has not received significantly more analysis than the Isogeny based scheme. In particular the work of Galbraith and Delfs from 2013 is an independent assessment of the difficulty of solving the underlying hard problem in the case of the Isogeny problem.
Many of the lattice schemes are designed and analyzed by the same small group of researchers who base their research on each others previous research. Of course research on the Isogeny key exchange is not immune from that. A more recent paper by Biasse and Jao on the difficulty of finding isogenies includes one of the inventors (Jao) as an author. Nevertheless, the Isogeny key exchange builds on almost two decades of intense research on elliptic curves. Until recently the only lattice based scheme under active scrutiny was NTRU and there the findings were historically problematic. Of course if efficiency is what you need, the lattice based schemes are indeed superior to the Isogeny based key exchange. I hope this helps.
You might want to write to Fishein, Jao, and Azarderakhsh to see if they posted their software anywhere. They claim to have software that is significantly more officient that the original code.