# Can binomial distribution be used to sample noise for Ring-LWE-based homomorphic encryption?

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?

• Yes. Though, this is only efficient for small standard deviation. – LeoDucas May 4 at 18:37