NewHope

Design choices

• Binomial Sampling: Although sampling to high-quality discrete Gaussian distribution is important in post-quantum lattice-based compact signature scheme such as Falcon and BLISS to prevent signature from leaking information about the private key, it's otherwise not so essential to key exchange schemes. The author chose to sample error vectors from binomial distribution.
• Error Reconciliation: What NewHope differs from its predecessors, is its method for error reconciliation. Previous ring learning with error key exchange schemes corrects errors one coefficient at a time; where as NewHope corrects error 2 or 4 coefficients at a time based on high-dimension geometry. This allows for lower decryption failure rate and higher security.
• Base Vector Generation: The authors of NewHope proposed deriving the base "generator" vector from the output of the XOF function SHAKE-128 in order to prevent "back-doored" values from being used, as may happen with traditional Diffie-Hellman through Logjam attack.
• Security Levels: In the early versions of the papers describing NewHope, authors proposed using 1024-degree polynomial for 128-bit "post-quantum" security level, and a 512-degree polynomial as "toy" instance for cryptanalysis challenge. In the version submitted to NIST, the 512-degree version is codified to provide 128-bit "classical" security level.