Difficult: The two methods for deciding if a number is a square mod another number (either prime or a non even composite of primes) is interesting, but does not seem very useful. As it mentions at the end, if we find that the Jacobi symbol of a mod n is +1, then we still do not really know if it is a square root, and should we decide that it is we have no way of finding what square root it is if we cannot factor n. Since the point was to have an n that is difficult to factor, this does not seem very useful. I appreciated that the section came out and said at the end that the Jacobi symbol does not give an answer to whether a is truly a square root or not. As it started that part of the section, it seemed to say that this would tell you whether a was or was not a square root mod n. In fact, even in the last example it seems to say this is true, so I might still be confused about it.
Reflective: We seem to be doing alot with prime numbers that seems to have no practical use in cryptography...yet. I'm holding out hope that we see the use of these symbols as we go on. It is nice to be able to quickly tell if something is a square root, but seems pretty useless in application given how the RSA system works. If I know it is a square root, how does that help me to break the code?
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