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I'm still not sure why it has highest entropy (higher than uniform distribution). What is the intuition of it?

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  • $\begingroup$ If a discrete gaussian and a uniform distribution have the same variance, then discrete gaussian would mathematically have higher entropy. $\endgroup$ – DannyNiu Aug 21 '17 at 4:30
  • $\begingroup$ Thanks! that's why gaussian is used in lattice based cryptosystem particularly homomorphic encryption. Homomorphic encryption has to manage encryption part with a bounded error term to ensure the correctness of decryption. The word "bounded" means that the error must be sampled from some specific range (defined by a variance). Based on variance, gaussian distribution is absolutely preferred! $\endgroup$ – mallea Aug 21 '17 at 4:51
  • $\begingroup$ @DannyNiu you said "mathematically", do you have some source of it? $\endgroup$ – mallea Aug 21 '17 at 4:52
  • $\begingroup$ It's mentioned here for continuous case, sources are cited by fellow Wikipedians. As for discrete case, I don't have known sources on hand, sorry. $\endgroup$ – DannyNiu Aug 21 '17 at 9:14
  • $\begingroup$ For the discrete case, I laid it out as Lemma 3.21 of homepages.cwi.nl/~ducas/Thesis/thesis.pdf . $\endgroup$ – LeoDucas Jul 8 '18 at 9:06

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