I think one of the things I was having difficulty understanding is why we're learning so much about factoring, when in practice, the kinds of integers that will actually be used in implementing RSA cannot be factored in time shorter than the life of the universe. Although when I think about it, they are important principles of number theory that I'm sure can help with understanding other concepts of cryptography.
I never would have imagined when I first learned about something as simple as factoring numbers that it could become impossible, at least in a reasonable amount of time for numbers with many digits. It seems like something that should be simple, like dividing or multiplying. The fact that it is so difficult is also good for cryptography since it makes RSA a useful algorithm. I guess one day when a way to factor massive integers has been discovered, we'll just have to start using a new algorithm. Although I have no idea how close that day actually is. That will be amazing though.
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