14.1 is on zero knowledge systems, which are really cool, and the diagram of the tunnel with the door really helps to understand the philosophy behind it. So, I claim that I can find square roots modulo n, I compute x1 and x2 and then send them to someone, who then asks me to tell him the square root of one of the numbers. I tell him the square root because I know it. If I did not know it, then he would know that I did not have the key, and would deny me access. If I am trying to fake it, I have a 50-50 shot of doing being able to fake it, but that is why the test is done multiple times. Because the chance of faking it decreases like powers of one half.
14.2 is the FFS method of this, which is the same except that it is done in parellel, where I send lots of x1,x2 pairs and am asked for the square roots of xi_k, where i_k is ramdomly a one or a two. Same chances as the previous scheme, 1/2 to the power of the number of square roots checked.
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