Homomorphic encryption schemes based on Ring-LWE need to sample the noise terms from a discrete probability distribution $\chi$ over the integers with support $[-B,B]$. For example, the Fan-Vercauteren encryption scheme uses the discrete Gaussian distribution.

Several Ring-LWE-based public key encryption and key encapsulation schemes, e.g., NewHope, Kyber, etc, use binomial distributions instead of discrete Gaussians since they are easier to sample from. Can a similar optimization be made for homomorphic encryption schemes?

  • $\begingroup$ Yes. Though, this is only efficient for small standard deviation. $\endgroup$ – LeoDucas May 4 '19 at 18:37

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