# multi-theorem vs single-theorem for non-interactive zero knowledge

I am trying to understand the definition of zero knowledge for non interactive zero knowledge (signature of knowledge). Sometimes I find multi-theorem zero knowledge, sometimes I find single-theorem. What's the difference ?

My main task is to show that a Zero Knowledge Signature of Knowledge which is zero knowledge (for one signature) is zero knowledge for several signatures. In other words, if you don't reveal anything by signing one message, you don't reveal anything if many people sign many documents with this ZKSoK.

• Could you add some references? – Occams_Trimmer Jul 10 '17 at 13:45

multi-theorem basically mean reusing proving & verification keys from Setup for unbounded number of rounds/repetition/theorem without compromising the soundness or zk. (i.e. reuse CRS for many $$x \in L$$)