This software is an implementation of the Ring Learning With Errors (RLWE) key exchange using the style guide from Open Whisper Systems. This implementation largely follows the one published by Singh and Chopra:

• "A Practical Key Exchange for the Internet using Lattice Cryptography" by Vikram Singh. http://eprint.iacr.org/2015/138
• "Even More Practical Key Exchanges for the Internet using Lattice Cryptography" by Vikram Singh and Arun Chopra. http://eprint.iacr.org/2015/1120.
• www.github.com/vscrypto/ringlwe

More recent work was published by Microsoft introducing additional optimizations for Number Theoretic Transform computations. These have now been incorporated making the average runtime per exchange about 2.75 times faster.

• "Speeding up the Number Theoretic Transform for Faster Ideal Lattice-Based Cryptography" by Patrick Longa and Michael Naehrig. https://eprint.iacr.org/2016/504.pdf.

With these optimizations, a new parameter has been introduced to facilitate compatibility between different Fourier optimizations. Keys can either be transmitted in the Fourier domain (for greater efficiency) or the Ordinary domain (for interoperability). Preliminary tests indicate that it takes about 1.17 times as long to complete an exchange transmitting in the ordinary domain than in the Fourier domain.

Note of caution: This implementation (and the RLWE key exchange in general) is not a drop-in replacement for ECDH. In ECDH, both parties generate a key pair, transmit their public keys, and compute the shared agreement from their own private key and the other party's public key.

   Generate key pair                               Generate key pair
   Transmit public key                             Transmit public key
   Wait (receive public key)                       Wait (receive public key)
   Agreement (their public, my private)            Agreement (their public, my private)

The only required synchronicity is that one must receive the other party's public key before computing the shared agreement. In RLWE, one party must compute the reconciliation data which both parties use for computing the shared key.

   Generate key pair                               Generate key pair
   Transmit public key
                                               Wait (receive public key)
                                               Compute rec data
					       Transmit public key and rec data
   Wait (receive pub key, rec data)                Agreement (their public, my private, rec data)
   Agreement (their public, my private, rec data)

Greater synchronicity is required and care must be taken when replacing an existing key exchange with RLWE.