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1

Not necessarily. For example, if there is a public-coin collision-resistant hash family then there is a (statistical) zero-knowledge argument system (with negligible soundness error) for NP that uses a constant number of rounds and has a public-coin verifier. However, in the random oracle model, constant-round public-coin computational zero-knowledge ...

1

As correctly pointed out by Ricky Demer it is not necessarily true. However, this implication does not hold for very specific cases. In the case of random oracle gates the existence of the RO changes the functionality of the "scheme", since with RO there are RO-Gates and without there aren't. In most cases the existence of the RO does not affect the ...

1

You always need to have in mind that $A$ is a hypothetical algorithm, since our goal in the reduction is to contradict the existence of such an efficient $A$. Now to your concrete security framework: Here, you are not satisfied by the fact that a hypothetical poly-time $A$ implies a poly-time reduction $A'$, but your aim is that the reduction does not take ...

4

The equation $t'=t+n\cdot t_c$ is an estimation to put an upper limit on $t'$. It might be possible that an attacker $A'$ can use a different, more efficient algorithm. But since the attack will work with using $A$, there exists an attacker $A'$ with at most $t'$. This means it's actually not an equation, but an inequality $t' \leq t + n \cdot t_c$. And then ...

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