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The zero-knowledge protocol you describe in your computation is an example of computational zero-knowledge. A more stringent requirement is statistical zero-knowledge, and the corresponding class of languages is $\mathsf{SZK}$. The classical example is graph non-isomorphism, see for example slides of Eli Biham. In fact, this protocol is perfect zero-...

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One of the most basic assumptions in cryptography is the existence of hard problems, even on a very conceptual level. For example, to establish a secure communication channel, you want your cipher to impose problems on eavesdroppers which they cannot solve. The problem is that the existence of hard problems generally has (severe) impact to questions in ...

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The work flow is as following: $A_{TM}$ is a turing machine, w is its input. Modified $A_{TM}$: add condition logic in front of it to construct a new turing machine $E_{TM}$. $E_{TM}$ takes input x, then the condition logic inside $E_{TM}$ first check if(w!=x) reject. If (w==x), let w = x, then feed w to $A_{TM}$. $A_{TM}$ may have three possible ...

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