Sections 6.5-7, 7.1, due October 28

I think that it is cool that PKC can be extended just a little more to provide digital signatures and verifications. I guess I never thought of using d to encrypt and e to decrypt, but of course it works exactly the same.

I am also very interested in learning about discrete logs. I don't exactly understand how they are used yet, or why it is hard to do them in reverse. I suppose, though, that we will be spending plenty of time on them in the future.

Section 6.3, due October 21

Oops. I read the wrong section last time. But I really liked this reading on primality testing. We talked about the jacobi symbols, but not really what they meant. It was neat to see how they fit into primality testing.

I am not really sure what "probably prime" means. I understood that if these tests told us a number was composite, then we knew that for sure. When using primes for an RSA encryption, I doubt that they just use a number that is pseudoprime, or even strong pseudoprime. What other tests do they do? Are they very complicated? I remember reading this last summer about some primality tests and they went way over my head.

Section 6.4.1, due October 19

I think that it is really interesting the methods that are devised to break any cryptological system. It takes a lot of ingenious thinking. It is the same in this case. My hat is off to whoever invented the Quadratic sieve.

Are we just going to be talking about the quadratic sieve? Or will we be talking about number field sieves as well. I get the concept of the quadratic sieve, but there is no way that I would be able to employ it to break a system.

Section 6.1, due October 9

I think that RSA is very elegant. I think it interesting it is from AES. While they are both secure encryption methods, they have almost nothing in common. While AES relies on confusion, RSA relies on only one thing: the difficulty of factoring large numbers.

I am pretty sure that they will talk about this in later chapters, but is it hard to find new primes to use. Obviously, a computer couldn't run through them all because there are so many. I just wonder if there are so many that you could not document them all.

Sections 3.6-7, due September 7

I think that generators are very interesting. I find it very surprising that there in no method to determine the generators of a field without actually testing them. I know it has been proven that one always exists and that there are Phi(p-1) of them but it seems that it shouldn't be that hard to tell which ones they are. But one thing about math is that the seemingly simple can be very complex and visa versa.

Was the three-pass protocol actually put into practice before RSA? Or was it just a stepping stone in PKC that was immediately followed by RSA?