1. The hardest part for me to understand was the first example they give us to examine. It was hard to follow where all the numbers were coming from and why they were substituting certain expressions for specific variables in various other expressions. I also didn't understand why they could say that the sum of the three roots is minus the coefficient of x^2. Then later in the reading it suggests that -4 is a double root. Yet earlier in the reading it suggested as a "technical point" that we wouldn't worry about multiple roots until 16.3.
2. When doing these readings, I like to predict how the new ideas and techniques being introduced are going to be used in cryptography. I'm guessing that somehow the author of a certain key is going to use a made up equation (made up according to certain guidelines). Then the author is going to pick two (possibly random?) points and use them to find the third point based on the line that goes through P1 and P2 as described in the text. The coordinates of the third point will then be used to create an encryption and decryption key. I don't know HOW the coordinates will be used (unless the original two points are chosen so that the third point is composed of two large random numbers and then we would be in the realm of RSA) but I'm pretty sure they will be used to create E[k] and D[k]. I'm guessing all this purely on the ideas we've discussed on public cryptosystems. The third point is easy to find only to the author of the equation of the elliptical curve. It would be nigh impossible for a random citizen to find the original two points based purely on the third point. This leaves me with the question, "what components will be made public? P3? P2 & P1?" My guess is P3. Then the author can use P1 and P2 to create a decryption key.
No comments:
Post a Comment