Paper 2015/889

Which Ring Based Somewhat Homomorphic Encryption Scheme is Best?

Anamaria Costache and Nigel P. Smart


The purpose of this paper is to compare side-by-side the NTRU and BGV schemes in their non-scale invariant (messages in the lower bits), and their scale invariant (message in the upper bits) forms. The scale invariant versions are often called the FV and YASHE schemes. As an additional optimization, we also investigate the affect of modulus reduction on the scale-invariant schemes. We compare the schemes using the ``average case'' noise analysis presented by Gentry et al. In addition we unify notation and techniques so as to show commonalities between the schemes. We find that the BGV scheme appears to be more efficient for large plaintext moduli, whilst YASHE seems more efficient for small plaintext moduli (although the benefit is not as great as one would have expected).

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. MAJOR revision.CT-RSA 2016
Contact author(s)
anamaria costache @ bristol ac uk
nigel @ cs bris ac uk
2015-11-23: last of 4 revisions
2015-09-14: received
See all versions
Short URL
Creative Commons Attribution


      author = {Anamaria Costache and Nigel P.  Smart},
      title = {Which Ring Based Somewhat Homomorphic Encryption Scheme is Best?},
      howpublished = {Cryptology ePrint Archive, Paper 2015/889},
      year = {2015},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.