16.1 Elliptic Curves: The Addition Law

• I have never heard of elliptic curves until this class so it was interesting to read about them. I am still kind of confused on what defines an elliptic curves.
• A few things I didn't understand about the reading is first of all, what is an abelian group? second, I was confused on the graph of y^2=x(x+1)(x-1). I'm not sure why there wasn't any values for x between 0 and 1.

2.12 Enigma

• I enjoyed reading about a cryptosystem that was used in WWII. It is always neat to get the history behind the cryptosystems and see how they were used. I also thought it was interesting that they used rotors that spun. It seems like the messages would be very long Vigenere ciphers but the key would be too enormous to do any frequency analysis or anything. So it seems kind of like a one time pad that was used for all the messages that day.
• It was hard to understand how the knowledge of the permutations helped break the system.

19.3 Shor's Algorithm

• I found it very interesting to learn more about what a quantum computer is. Although I feel like I still don't understand it, it was cool to learn more about it.
• I understand that Shor's Algorithm says that if we find the period, we can use that to factor n. But I was pretty confused on how that works and how the use of a quantum computer would help in finding the period.

19.1 & 19.2 Quantum Techniques in Cryptography

• The most interesting part of this section was reading about quantum mechanics. I don't really know anything about it but I found it interesting to learn a little. I also thought that it was cool to see why in the experiment using two filters blocked all light but using three filters let 1/8 of the light in.
• The hardest part to understand was why Bob has 25% chance of measuring the incorrect value. It seems to me that it should be more like 25% chance of measuring the correct value.

14.1 & 14.2 Zero-Knowledge Techniques

• The whole idea of convincing someone that you know something or can do something without giving away information is pretty interesting. It reminds me of those puzzles where you try getting the ring off. Whenever you finish, your friend wants to see if you can do it but you don't want to show him how to do it. It reminds me of that.
• The Feige-Fiat-Shamir Identification Scheme was pretty confusing. I didn't understand how they set up a single identification scheme or what that exactly meant.

12.1-12.2 Secret Sharing Schemes

• I thought that this section was interesting because it provides an interesting question, how to hind information so that people have to collaborate in order to solve the problem.
• The hardest part to understand was the Shamir threshold scheme. It wasn't hard to understand, it was just harder to understand than the method. The hardest part to understand was how to hind a meaningful message but it made sense after doing the reading.

Test Review

• I think the most important thing we have studied is the RSA because we've spent the most time on it by far. Digital signatures also seem important but not nearly as much as RSA.
• I expect there to be questions asking to prove why m^(e*d) is congruent to m. I also expect to see questions asking how to decrypt messages that have been encrypted wrongly.
• I feel like I need to remember the special tricks to factoring n, like the p-1 method and the Quadratic Sieve and the primality Test. I also feel like I need to understand the Discrete Logs and the Hash functions better.
• So far, I've really enjoyed learning about RSA and digital signatures. I don't know what else there is to learn in those subjects but they've been the most interesting to me thus far.

8.3 & 9.5 The Secure Hash Algorithm & The Digital Signature Algorithm

• The digital signature algorithm was much more interesting than the secure hash algorithm because it was easier to understand. It was very similar to the ElGamal signature.
• The secure hash algorithm was very hard to understand. I got confused on the specific steps of the algorithm; other than that, I think I understood.

9.1-9.4 Digital Signatures

• I thought the RSA signature part was really interesting. It was cool to think about proving that you discovered something without actually telling anyone what you did. I also found it interesting to see how to use the birthday attack to get a fraudulent signature.
• I'm still a little confused on how the hash functions work and how they're secure. I think I need to see an example of one to understand it better. The ElGamal Signature Scheme was also a little confusing but I think I understood it after a while.

8.4-8.5,8.7 Birthday Attacks, Multicollisions, Using Hash Functions to Encrypt

• I thought it was fascinating learning about the statistics of finding a pair of birthdays in a group of thirty or the odds of finding two license plates with the last 3 digits. I thought this was very cool. I also enjoyed learning about how to use hash functions although I didn't understand it all completely.
• The most difficult part to understand was the Multicollisions section. I was very confused on how the we could find multiple messages that have the same hash function. I didn't really understand it.

8.1-8.2 Hash Functions, A Simple Hash Example

• I was pretty confused on why we would want to implement a hash function. Obviously there would be speed advantages to sending less information but I didn't understand why we would cut out information from our message to do this.
• I guess the most interesting part, although I didn't understand why we did it, is that we could send a shorter message and save time. We can also use this for digital signatures, which I'm interested in learning about.

7.3-7.5 Bit Commitment, Diffie-Hellman Key Exchange, and The ElGamal Public Key Cryptosystem

• I thought the part about predicting football game outcomes was very interesting. It put an interesting perspective on the topic of sending a message that can't be changed but needs to be deciphered by the sender.
• I didn't really understand the difference between the Computational and Decision Diffie-Hellman Problems.