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Complexity describes - in simple words - how hard (complex) it is to reach a specific goal; and under which conditions. In cryptography, this mostly ends up in using the complexity theory to analyze things. One of the main goals of complexity theory is to prove lower bounds on the resources (e.g. time and/or space) needed to solve a certain computational problem. Cryptography can therefore be seen as the complexity theory's main field of use.

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Show that there is an efficient zero knowledge proof for any language $L \in NP$

Let $(P,V)$ be an efficient zero-knowledge interactive proof for some language $A \in NP$ that is $(T,\epsilon)-\text{sound}$ and $(T,\epsilon)-\text{ZK}$. I want to show that for every language $L$ t …