# Is SZK better than CZK?

Is it better to have statistical zero-knowledge or computational zero- knowledge in a system?

If it depends, is there a slightly accurate generalisation that can be made?

Maybe one can be somewhat reduced to the other (doubt it)?

Maybe one of them solves a larger class of problems?

• Discourse: SZK can only be broken if the protocol is ran exp amount of times/enough times to take advantage of the statistical difference. While CZK needs to be ran by an unbounded/exponential TM. Intuition is telling me that SZK is "close enough" to PZK that it does not matter, but they both seem breakable if given an unbounded TM... – WeCanBeFriends Aug 22 '19 at 22:49

Security-wise having statistical security is always better than computational security if the security parameter is equal. This is because statistical security ($$\forall A: Pr[A(f(x)) = x] \le negl(n)$$) implies computational security ($$\forall B: Pr[B(f(x)) = x] \le negl(n)$$) with B all algorithms in P-SPACE and A being all algorithms (which includes all algorithms in B).