section 16.5

Difficult: I'm a little confused about the El Gamal with elliptic curves.

Interesting: It's interesting how fairly simple it is to convert these systems into elliptic curves

section 16.4

Difficult: I'm still confused about what omega is in GF(4).

Interesting: The fact that finding -P from P in mod 2 is different than other cases is interesting to know.

section 16.3

Difficult: I don't think I really understood how to find the factors using elliptic curves very well.

Interesting: I thought the idea of smooth and b-smooth numbers was interesting since I've never really learned about them before by name. I didn't know there was a name for those numbers! I think it's pretty awesome that someone cared about them enough to name them, though I do wonder why they chose those names.

section 16.2

Difficult: Discrete logarithms sound like they would be difficult to do with elliptic curves.

Interesting: It's interesting that there's a way to use elliptic curves to encode/decode messages. In all honesty, before that last bit of the section, I was like, what the heck does this have to do with cryptography. And now I am beginning to see the possibilities. Pretty cool how people can come up with these ideas for cryptosystems.

section 16.1

Difficult: I'm not sure I understood the adding points part very well.

Interesting: the whole concept was interesting since I've never learned about it before that I can remember, but I don't really get what this has to do with Cryptography.

sections 18.1 and 18.2

Difficult: I didn't understand the Hamming distance very well.

Interesting: It's interesting that they've come up with a way to correct errors in code words, etc.

section 2.12

Difficult: I didn't understand the process very well for attacking it

Interesting: It's funny that this is what our reading is for tomorrow since I was actually just talking to someone about Enigma earlier today when I told them I was in a Cryptography class. I think it's interesting (though I guess unsurprising) that the British sold captured machines to former colonies and kept the fact that they had broken it a secret for so long.

Shor's algorithm and section 19.3

Difficult: Shor's Algorithm and the quantum Fourier transformation was kind of confusing

Interesting: The whole idea of a quantum computer was interesting. Especially since the authors said that they aren't yet a reality and yet the ideas are out there on what the computer would be able to do even though it isn't a reality. Also, the internet reading will really interesting to read. Definitely sounded like something you would have written just because of the guy's personality...

sections 19.1 and 19.2

Difficult: It doesn't seem that difficult as far as the key distribution part goes, but I'm still confused about quantum mechanics itself

Interesting: It's really weird/interesting to find out that quantum mechanics has applications in cryptography. The filter/overview of quantum mechanics discussion was interesting

sections 14.1 and 14.2

Difficult: I don't think I understood very well what the heck was going on with the tunnel analogy. how can Peggy always come up the correct side of the tunnel if she doesn't know which way the door opens? I'm confused.

Interesting: the story at the beginning was interesting. It's weird that someone could manage to put a fake atm anywhere period without security/mall officials or whoever asking questions to validate that the machine was legitimate.

Midterm 2 Review

• Which topics and ideas do you think are the most important out of those we have studied?
• What kinds of questions do you expect to see on the exam?
• What do you need to work on understanding better before the exam?
Thinking about the answers to these questions can help guide your study.

I don't know how to solve any of these problems by hand very well at all!! Please go over that in class!

sections 12.1 and 12.2

Difficult: I'm not sure I understand the Shamir threshold scheme very well, but I'm sure with pracetice, I'll be able to understand it better

Interesting: I like the whole you need two people to reconstruct idea. It's a lot like how you need multiple keys to set off those crazy bombs the military uses, etc. I like that it makes it harder for people to find since the pieces are divied up.

sections 9.1-9.4

Difficult: Are we going to have to break any of these? Because I'm not sure I'd be able to until possible after reading later sections that probably go into methods to break them. Though I'm sure they are similar to how we break RSA and ElGamal. I also thought the ElGamal Signature Scheme was kind of complicated, but still kind of like the normal ElGamal encryption method, so maybe it's not as bad as it looks? Could you do examples of these methods in class?

Interesting: I thought it was interesting how the different encryption methods could be modified to create personalized signatures and also that this idea hasn't (explicitly) come up before these sections really. I also thought the difference between the signature with appendix and message recover scheme was interesting.

sections 8.4-8.5 and 8.7

Difficult: I'm kind of confused about how to use the birthday idea to attack different ciphers

Interesting: I found it interesting that they spent so much time talking about the probability of repeating birthdays when almost everyone already knows about the birthday paradox.

sections 8.1-8.2

Difficult: I thought the second hash method would be difficult to do--for long messages, especially.

Interesting: I thought the hash function in 8.2 was interesting because it was more effective than the first one described, I wonder what other hash methods there are that would be more effective.

sections 7.3-7.5

Difficult: I think the Diffie Hellman Key Exchange would to interesting and difficult to encrypt/decrypt by hand for sure, but I also think the Computational Diffie-Hellman Problem would be difficult to compute period. Could you show an example in class?

Interesting: The bit commitment section was really interesting. I had never really thought of it before, but it makes since in some situations that someone would make a bet/prediction or something like that and would not want the other person to know what they sent until a certain day/time. It's kind of like sending a gift before someone's birthday and not wanting them to open it until their birthday, even though it was sent early. I think it's a really cool way to accomplish this, because before, you just had an honor system so to speak, but this way, you can't change the bet/whatever, and Bob can't open it until you give him the 'key' so to speak.

section 7.2

Difficult: I still don't think I understand their notation very well, the whole x = L sub alpha (beta) thing is hard for me to keep track of which part means what,but I'm sure time/hw problems will help with that so I can keep them all straight. Are we going to be expected to factor all these bigger numbers and mod them in our heads/using only a basic calculator on the next exam? Because I'm pretty sure that would extend the amount I need to set aside for the test substantially.

Interesting: The Baby Step, Giant Step Attack was pretty interesting. I also thought the fact that they named the attack that was pretty funny. But it is cool that/interesting to think about since the two lists are interconnected and there's a match, but since it only works well for primes up to 10^20, it makes me wonder what a better method would be.

Sections 6.4.1 & 6.4.2

Difficult: I didn't understand the part about linear dependencies very well in 6.4.1. I'm also not sure I understood the matrix connection very clearly.

Interesting: it is really interesting how far we've come with factoring algorithms in the last 30 or so years and how big of an impact computers have had on our mathematical and other advances. Who knew such a relatively small thing would have such far reaching impacts?! It's pretty cool, not going to lie.

PS, as you can see below, I accidentally posted the entry on my personal blog instead of my Cryptography blog--sorry!!

sections 6.5-6.7 and section 7.1

Difficult: The discrete logarithm problem looked difficult, I didn't understand very well why n had to be the smallest positive integer such that alpha^n is congruent to 1 mod p for us to get that x=(L_alpha)(beta) though. Could you explain why in class?

Interesting: It's crazy how many people and computers it took to find the congruence relations of the desired type for this problem! and then how relatively they were able to reduce the matrix and determine the dependencies. I also thought the message was pretty interesting... mostly weird, but I guess it makes sense since they didn't want anyone to just arbitrarily guess what it was and get the moneys without doing the work.

6.4 up to just before section 6.4.1

Interesting: I think it's crazy how many awesome ideas Fermat came up with. Seriously, were all of these ideas actually his or did he just steal it from people who didn't care to publish or is some of his work actually someone else's that historians decided to attach his name to? But I guess when you think about Euler, Fermat's work pales in comparison as far as breadth goes. Still, Fermat had some pretty crazy ideas and theorems. I do like that there are other methods of factoring large numbers other than checking every prime up to and including the square root of the number, because for large numbers, it's impractical to do this.

Difficult: I'm not sure that I understood the p-1 factoring algorithm very well or at least I don't know how we would know if we picked a "good enough" a and bound B for the algorithm. Also, how would we know when to stop computing?