1. The interesting part of this was the relation to Signatures (El Gamal) but more especially, how easy and convenient the diffie hellman key exchange becomes.
2. The hard part was understanding El Gamal Digital Signatures for elliptic curves.
Saturday, December 1, 2012
16.4, due Monday Dec 3rd
1. The hard part about this was following the example all the way through. It just took a little extra time to figure out what was going on.
2. The interesting part was how secure systems can be mod 2 or mod 2^n. I thought this would either decrease the security of the system, or make it difficult to represent points, but both challenges are overcome.
2. The interesting part was how secure systems can be mod 2 or mod 2^n. I thought this would either decrease the security of the system, or make it difficult to represent points, but both challenges are overcome.
Friday, November 30, 2012
16.3, due Fri Nov 30
1. I thought the difficult part of this reading was understanding "smoothness." I didn't understand why it is best suited for medium numbers either.
2. I really liked the analogy of the p-1 method to factoring elliptic curves. Although does that make elliptic curve cryptography weaker because all a hacker has to do is try several curves to factor n? I thought singular curves were interesting.
2. I really liked the analogy of the p-1 method to factoring elliptic curves. Although does that make elliptic curve cryptography weaker because all a hacker has to do is try several curves to factor n? I thought singular curves were interesting.
Monday, November 26, 2012
16.2, due Wednesday November 28th
1. It wasn't really difficult this time but I do have one question: Why would it be useful to approximate (or know) how many points are on an elliptic curve? I assume these methods are only valuable for finite fields...not for the reals or complex numbers etc.
2. I liked how previous methods apply to elliptic curves for trying to crack them. I thought it was interesting the index calculus approach doesn't work though.
2. I liked how previous methods apply to elliptic curves for trying to crack them. I thought it was interesting the index calculus approach doesn't work though.
Wednesday, November 21, 2012
16.1, due Monday Nov 26
1. I didn't understand the addition of points. It seems to me to be the addition or product of 'lines' more than points.
2. I thought it was amazing that you can find a third point given two (or even one!) points by using the formula they give.
2. I thought it was amazing that you can find a third point given two (or even one!) points by using the formula they give.
Monday, November 19, 2012
Online reading and 19.3, due Monday Nov 19
1. I didn't understand the "linear combination of states" part. The Discrete Fourier Transform was tricky to understand, both the process and the reason.
2. I liked the online reading a lot. The example of a tackboard showing what period he was on was awesome! I also thought it was interesting how quantum computers could factor large numbers.
2. I liked the online reading a lot. The example of a tackboard showing what period he was on was awesome! I also thought it was interesting how quantum computers could factor large numbers.
Friday, November 16, 2012
19.1 and 19.2, due Friday Nov 16th
1. I didn't understand any of this reading. I think I could understand it better if I knew how light worked.
2. The idea of sending photons and having such a thing as quantum computers was interesting. I liked how it again, similar to chapter 14, covered probabilities. The additional reading was very insightful.
2. The idea of sending photons and having such a thing as quantum computers was interesting. I liked how it again, similar to chapter 14, covered probabilities. The additional reading was very insightful.
Wednesday, November 14, 2012
14.1 and 14.2, due Wednesday Nov 14th
1. I didn't understand the steps of 14.2 super well. Basically, how Victor's check allows him to accurately guess that Peggy knows, s sub i.
2. Fascinating! Zero knowledge proofs are cool! Victor will never know both square roots of x1 and x2 and so cannot deduce sqrt of y :)
2. Fascinating! Zero knowledge proofs are cool! Victor will never know both square roots of x1 and x2 and so cannot deduce sqrt of y :)
Monday, November 12, 2012
12.1 and 12.2, due Monday Nov 12
1. The hardest part about today's reading was focusing on it instead of studying for the test.
2. I liked the concept of secret sharing and being able to share the secret and make it known with only a handful of people.(section 12.2)
2. I liked the concept of secret sharing and being able to share the secret and make it known with only a handful of people.(section 12.2)
Friday, November 9, 2012
Q & A, due Friday November 9
1. I think the most important topics on exam 2 will be RSA and different decrytping techniques, discrete log problem and other related things like El Gamal, how to use a hash function correctly, and possibly something about a signature. Probably some relatively simple proof from chapter 3.
2. I need to review all of it. The Project 12 and recent homework assignments, etc. I'm much more nervous for this test than I was for the first...
2. I need to review all of it. The Project 12 and recent homework assignments, etc. I'm much more nervous for this test than I was for the first...
Wednesday, November 7, 2012
8.3 and 9.5, due Wednesday November 7
1. I thought it was difficult to understand section 9.5.
2. I liked the similarity of sha to des. A lot of the same operations are used
2. I liked the similarity of sha to des. A lot of the same operations are used
Sunday, November 4, 2012
9.1-9.4, due Monday November 5
1. Cryptography is a fascinating thing. I couldn't find anything difficult in this reading except for how all of this was discovered/thought of. :D
2. I liked the reading of birthday attacks on signatures and wonder how often we are being handed such electronic documents that have fraudlent equivalents(as far as their hashes go). I thought the RSA signature was very concise but I hypothesize that if you were to combine it with a hash function you would be unable to retrieve the message(i.e. message recovery scheme would fail to work) I like it better than El Gamal and don't remember in which situations El Gamal is advantageous over RSA.
2. I liked the reading of birthday attacks on signatures and wonder how often we are being handed such electronic documents that have fraudlent equivalents(as far as their hashes go). I thought the RSA signature was very concise but I hypothesize that if you were to combine it with a hash function you would be unable to retrieve the message(i.e. message recovery scheme would fail to work) I like it better than El Gamal and don't remember in which situations El Gamal is advantageous over RSA.
Thursday, November 1, 2012
8.4-8.5 and 8.7, due Fri Nov 2
1. I didn't understand why concatenation of hash functions does not apparently strengthen its preimage resistance. Or how they derived running times to find collisions.
2. I loved reading about the birthday paradox. I told my wife and she was (and I think still is skeptical that the chances are that high haha). 8.4.1 reminded me of BSGS.
2. I loved reading about the birthday paradox. I told my wife and she was (and I think still is skeptical that the chances are that high haha). 8.4.1 reminded me of BSGS.
Wednesday, October 31, 2012
8.1 & 8.2, due Wednesday October 31
1. The tricky part about understanding the reading was 8.2
2. 8.1 was really interesting especially because of the three properties it explained in the section
2. 8.1 was really interesting especially because of the three properties it explained in the section
Sunday, October 28, 2012
7.3-7.5, due Monday October 29th
1. I didn't understand the difference between solving the decision vs computational diffie-hellman algorithm.
2. I really enjoyed bit commitment although I don't see how it applies much other than betting situations. I liked how they explained El Gamal and its similarity to RSA.
2. I really enjoyed bit commitment although I don't see how it applies much other than betting situations. I liked how they explained El Gamal and its similarity to RSA.
Thursday, October 25, 2012
7.2, due Fri October 26th
1. I didn't understand the pollhig-hellman? thing very well. I don't remember what the "pi" looking symbol means and how to compute it.
2. I really liked the part where it talks about discrete logs for the case of 3 mod 4 and the description on how to compute them was done quite well.
2. I really liked the part where it talks about discrete logs for the case of 3 mod 4 and the description on how to compute them was done quite well.
Tuesday, October 23, 2012
6.5-6.7, 7.1, due Wednesday October 24th
1. I didn't understand discrete logs at all. Hopefully they aren't that hard :s
2. I liked how it discussed what was necessary to have a public key cryptosystem. I also enjoyed reading the history in 6.5 of the rsa challenge and it's application to treaties.
2. I liked how it discussed what was necessary to have a public key cryptosystem. I also enjoyed reading the history in 6.5 of the rsa challenge and it's application to treaties.
Thursday, October 18, 2012
6.4.1 and 6.4.2, due Monday October 22
1. I didn't like the Theoretical Methods because they were so similar to the Miler-Rabin tests and I didn't really understand those too well:( also how does on quickly find summed vector rows congruent to 0 mod 2?
2. I really liked the idea of being able to factor n by finding several squares, each congruent to some factorization of small primes. This was interesting to me and I wondered how often it can be effective.
2. I really liked the idea of being able to factor n by finding several squares, each congruent to some factorization of small primes. This was interesting to me and I wondered how often it can be effective.
6.4, due Oct 19th
1. I didn't understand the p-1 factoring algorithm hardly at all. Conceptually or in practice. I also don't remember if for the Fermat factorization if we have discovered how to know what integers squared are mod p. Like for the example, how did we know 295927 + 3^2 = 544^2 mod 295927 (without simply squaring 544 of course)?
2. I really like the Fermat method of factorization. Once we compute n + 1, n + 4, n + 9, etc. and find which is congruent to a square mod n, the process is very very simple :)
2. I really like the Fermat method of factorization. Once we compute n + 1, n + 4, n + 9, etc. and find which is congruent to a square mod n, the process is very very simple :)
Tuesday, October 16, 2012
6.3, due Wednesday Oct 17th
1. I thought it was difficult to follow the examples about how to determine whether a number is probably prime or definitely composite. The last theorem's example specifically.
2. I liked how someone has found a deterministic algorithm to test primality of n; it makes RSA much more secure that factoring n is much more difficult than testing for primality...thank goodness:)
2. I liked how someone has found a deterministic algorithm to test primality of n; it makes RSA much more secure that factoring n is much more difficult than testing for primality...thank goodness:)
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