(Difficult) Th hardest part of this section to understand was where the author came up with the original squares he was using in the start of the section. If I understand it correctly, he takes squares which are just beyond n, so that they are small (mod n). This sounded alot like the what we did in class a few days ago, but the book's explanation seemed a little out of order. The book sort of pulled the squares out of thin air, then tried to explain them later. Was this method similar to the Fermat Factorization method? Finding values close to n, such as n + 1^2, n + 2^2, etc. until we found a square? it seems this method would also yield similar squares that would be small (mod n), which should give us relatively small prime factors.
(Reflective) I liked the table included in the book about the number of digits of factorization records over the last few decades. Clearly RSA has had a great influence on the study of factoring, and even today people continue to develop or improve existing methods of factoring. This is a great example of what interests me the most about cryptography: Cryptography continues to expand, and the study of cryptography is always new, and always interesting. Even though the math community has a great understanding of encryption methods, there is always more to learn, more to explore. It leaves open a great deal of opportunity for continued research, for greater understanding, and continued education. As I get closer to graduation, I realize I want to get into a career that always me to further my education, to always be pushing my self and my mental capacity a little further.
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