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NewHope: Quantum-robust Crypto for Key Generation using Ring Learning With Errors

Prof Bill Buchanan OBE FRSE
Published in
5 min readAug 6, 2018


A demo of this method is defined here.

There are several methods defined for quantum robust cryptography including:

  • Lattice-based cryptography [Lattice] — This classification shows great potential and is leading to new cryptography methods, such as for fully homomorphic encryption, and code obfuscation.
  • Code-based cryptography [McEliece] — This classification was created in 1978 with the McEliece cryptosystem but has barely been using in real applications. The McEliece method uses linear codes that are used in error correcting codes, and involves matrix-vector multiplication. An example of a linear code is Hamming code.
  • Multivariate polynomial cryptography [UOV] — This classification involves the difficulty of solving systems of multivariate polynomials over finite fields. Unfortunately, many of the methods that have been proposed have already been broken.
  • Hash-based signatures [GMSS] — This classification involves creating digital signatures using hashing methods. The drawback is that a signer needs to keep a track of all of the messages that have been signed, and that there is a limit to the number of signatures that can be produced. New methods, though, integrate into Merkle Trees, which allows for the…



Prof Bill Buchanan OBE FRSE

Professor of Cryptography. Serial innovator. Believer in fairness, justice & freedom. Based in Edinburgh. Old World Breaker. New World Creator. Building trust.