1. I had a difficult time understand the last two large paragraphs of 16.5. I don't get why integers mod p are replaced with the curve and why the number p-1 becomes n. I also don't get why "the use of the x-coordinate in the elliptic version is somewhat arbitrary", but at the same time "using the x-coordinate is an easy choice." Where does the x-coordinate come from?
2. I was really interested to read the last part of the section that shows that k*k^-1 was not 1 but was an integer congruent to 1 mod n. This proved that k*k^-1*A = A, even though it was not in the way I was originally thinking. I also was interested to see how elliptic curves could be used for encryption, key exchange, and digital signatures. While I know there has been a lot of study of cryptography, I would be interested to see if there are any other aspects of mathematics that could be used for cryptography.
I did the course evaluation.
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