I'm working on a P2P communications and chat framework, and am looking for a quantum-secure asymmetric key exchange algorithm which I can use to perform a key exchange of an AES-256 bit key. This is an open-source project which will be licensed under GPL-3.0, and I have considered using NTRU. However; I have discovered that NTRU is a patented cryptosystem, and is therefore not compliant with the licensing constraints that apply to my application. Are there any asymmetric key exchange systems other than NTRU which are not patent encumbered, and secure against quantum attacks?
UPDATE in response to NTRU answer
Turns out that the patent grant may not be in fact in compliance with the GPL. The patent grant document the answer refers to (PATENTS.md) states that
Businesses and enterprises that wish to incorporate NTRU cryptography into proprietary appliances or other commercial software products for re-distribution must have a commercial license
In contrast to the GPL, which permits commercial usage of a work if the commercial product is also licensed under the GPL. See the official FAQ on the matter of commercial use. This same FAQ page also clarifies, under a different section that the licensor cannot ban commercial/military use of a GPLd work as doing so is contradictory to the GPL.
UPDATE 2 -- Response from Security Innovation
The issue regarding GPL compliance has been sorted out. Below is an e-mail I have received clarifying the issue. I have decided to use NTRU under the GPL in my solution, and will be marking this answer as accepted.
Thanks for getting in touch. You're absolutely right, our patents.md file isn't correct: it specifies GPL but then contrasts GPLed use with commercial use of the patents, even though as you point out commercial use isn't precluded by GPL. So our patents.md file is not in fact consistent with GPL 2.0. This was an oversight on our part. The intent was to have language identical to what's in our licence.md file at https://github.com/NTRUOpenSourceProject/ntru-crypto/blob/master/LICENSE.md, specifically: "Parties who wish to distribute ntru-crypto, or components thereof, under licenses other than the GPL or the FOSS Exception must obtain a commercial license." This wording makes it clear, I hope, that in this context we use "commercial license" to mean "license for non-GPLed use". The intent is to be fully GPL compliant, including supporting commercial use under GPL. I'll work to get this language clarified on the site. Thanks for your eagle eyes, this is a good one to get sorted out. Hope this helps and let me know if you have any more questions. Cheers, William