1. The lecture was primarily on Prime Numbers. There wasn't anything TOO new in the lecture. He talked mostly about the mystery behind some patterns contained within prime numbers and then focused the remainder of the time on the RSA cryptosystem. One thing that is hard for me to fathom is how simple prime numbers are, yet how hard the research on them is. For instance, why is it so hard to find the next prime number? Isn't it just the next non-crossed off number using the Eratosthenese Sieve? Or why is it so hard to explain why factoring large numbers is hard. I know it's hard, but why is it hard to explain?
2. Something rather interesting about the presentation was contained in one sentence the presenter used: "Prime numbers are like atoms." He was saying that every number that isn't prime can be broken down into its key component numbers that ARE prime. I had never thought about prime numbers like this, but now that's pointed out, I like the comparison.
Tuesday, December 7, 2010
Section 16.5 Due 8 Dec 2010
1. The reading was simply an application of elliptical curves combined with cryptosystems we've already covered in the course. There wasn't anything TOO difficult about that. There was one thing, however. I didn't really understand WHY the verification step works in the ElGamal Digital Signatures application of elliptical curves. Also, I think I'm just over analyzing the reading, but it is very explicit in pointing out the fact that k^-1*k is not 1 but is congruent to 1. I don't understand why they're pointing that out here. I thought that was made clear in the beginning of the book. As such, I'm worried I'm missing something.
2. The thing I thought about most in relation to this reading was why would we use Elliptical Curves in a situation rather than using one of the original cryptosystems we've discussed. That is, why use the Elliptical Curve version of ElGamal rather than just plain old ElGamal? The question is, what advantages does one have over the other?
2. The thing I thought about most in relation to this reading was why would we use Elliptical Curves in a situation rather than using one of the original cryptosystems we've discussed. That is, why use the Elliptical Curve version of ElGamal rather than just plain old ElGamal? The question is, what advantages does one have over the other?
Thursday, December 2, 2010
Section 16.3 Due 3 Nov 2010
1. Two things I don't really understand. Toward the beginning of the reading it uses the denominator of the slope between two points to find the gcd between it and the number trying to be factored. I don't think I really understand WHY they use the denominator of the slope. After reading it through a few times, it seems like they did this because they were trying to find the inverse of 1770. Nonetheless, I'm not sure how this leads to using it to find the factorization of 2773. Then later in the reading, toward the end, they mentioned that this method is similar to finding gcd(1,n) and gcd(2,n) and so forth. It's probably not a big deal, but I don't see how they are related.
2. It's not too difficult but I'm interested in knowing more about the difference between "smooth" and "B-smooth." Again, it's probably not a big deal, but I have this thing with somewhat ambiguous definitions. Who's to say what are "only small prime factors" and what's not? Where is the line drawn?
2. It's not too difficult but I'm interested in knowing more about the difference between "smooth" and "B-smooth." Again, it's probably not a big deal, but I have this thing with somewhat ambiguous definitions. Who's to say what are "only small prime factors" and what's not? Where is the line drawn?
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