What was the most difficult part of the material for you?
As it was a talk, there were a lot of various Theorems that were mentioned. I would say understanding them all in that context would be fairly difficult.
What was the most interesting part of the material?
I thought that the Toa Theorem was very interesting. It is really cool to see all the crazy things people can think up. As well, there was a very very large number that was cool, (and thought to be prime.)
Tuesday, December 4, 2012
16.5, due 5 December
What was the most difficult part of the material for you?
The subtle point mentioned on page 366 was a little interesting. I had to think about why we could use inverses, like they said.
What was the most interesting part of the material?
I think it is very interesting how elliptic curves are so similar to discrete logs. I think it is cool that you can use either method, and to see that each has their various advantages and disadvantages.
The subtle point mentioned on page 366 was a little interesting. I had to think about why we could use inverses, like they said.
What was the most interesting part of the material?
I think it is very interesting how elliptic curves are so similar to discrete logs. I think it is cool that you can use either method, and to see that each has their various advantages and disadvantages.
Monday, November 26, 2012
16.2, due 28 November
What was the most difficult part of the material for you?
This section begins to map ideas used in the past onto elliptic curves. Sometimes it was difficult to fully make the crossover in my mind.
What was the most interesting part of the material?
I found the difficulty of attacking elliptic curves interesting. I think it is cool that some of the attacks that work on a discrete logarithm do not work on elliptic curves. They seem to be very interesting mathematical objects.
This section begins to map ideas used in the past onto elliptic curves. Sometimes it was difficult to fully make the crossover in my mind.
What was the most interesting part of the material?
I found the difficulty of attacking elliptic curves interesting. I think it is cool that some of the attacks that work on a discrete logarithm do not work on elliptic curves. They seem to be very interesting mathematical objects.
Tuesday, November 20, 2012
16.1, due 26 November
What was the most difficult part of the material for you?
The idea of elliptic curves is new to me. Thus, thinking about all the different intricacies was the most difficult part for me.
What was the most interesting part of the material?
I think using elliptic curves for cryptography is very interesting. I am excited to see how they play out and what we will be able to do with them.
The idea of elliptic curves is new to me. Thus, thinking about all the different intricacies was the most difficult part for me.
What was the most interesting part of the material?
I think using elliptic curves for cryptography is very interesting. I am excited to see how they play out and what we will be able to do with them.
Monday, November 19, 2012
Enigma machine, due 20 November
What was the most difficult part of the material for you?
I like thinking about all the challenging mechanical problems faced by the code crackers. Today, I would think "hey let's write a program". However, they actually had to build machines that would do this.
What was the most interesting part of the material?
I find it very interesting the vast variety of sources that helped to crack the code in this "real world" example. It was not just a single equation or method. It was a tireless back in forth of finding out more information, implementing it, working hard to brute force some things, coming across another piece of valuable information, etc.
I like thinking about all the challenging mechanical problems faced by the code crackers. Today, I would think "hey let's write a program". However, they actually had to build machines that would do this.
What was the most interesting part of the material?
I find it very interesting the vast variety of sources that helped to crack the code in this "real world" example. It was not just a single equation or method. It was a tireless back in forth of finding out more information, implementing it, working hard to brute force some things, coming across another piece of valuable information, etc.
Friday, November 16, 2012
19.3 and online reading, due 19 November
What was the most difficult part of the material for you?
I am still wrapping my head around the ket notation. As well, the quantum Fourier transform was difficult to understand.
What was the most interesting part of the material?
I think it is really interesting how quantum computers change the computing paradigm. I liked how the online article pointed out that it is not simply a super-parallel computing device. There are still considerations we must have, and we must still understand how to exploit the structure of the problem we are solving.
I am still wrapping my head around the ket notation. As well, the quantum Fourier transform was difficult to understand.
What was the most interesting part of the material?
I think it is really interesting how quantum computers change the computing paradigm. I liked how the online article pointed out that it is not simply a super-parallel computing device. There are still considerations we must have, and we must still understand how to exploit the structure of the problem we are solving.
Thursday, November 15, 2012
19.1-19.2, due on 16 November
What was the most difficult part of the material for you?
The Quantum mechanics. I didn't follow everything about the different bases, etc.
What was the most interesting part of the material?
I think the idea of Quantum computing is very exciting and interesting. It seems like it would change a lot of how we do things. I am hopeful that we will see them come to fruiting sometime in our lives.
The Quantum mechanics. I didn't follow everything about the different bases, etc.
What was the most interesting part of the material?
I think the idea of Quantum computing is very exciting and interesting. It seems like it would change a lot of how we do things. I am hopeful that we will see them come to fruiting sometime in our lives.
Monday, November 12, 2012
14.1-14.2, due on 14 November
What was the most difficult part of the material for you?
The Feige-Fiat-Shamir Identification Scheme is a little interesting. The trickiest part was understanding how Eve might be able to get away with certain selections of x if she knows the bitstring beforehand.
What was the most interesting part of the material?
I think the idea of zero-knowledge techniques is very fascinating. I think it is very cool that there is a scheme where one can identify oneself without revealing any part of the secret, and that the verifier can be satisfied.
The Feige-Fiat-Shamir Identification Scheme is a little interesting. The trickiest part was understanding how Eve might be able to get away with certain selections of x if she knows the bitstring beforehand.
What was the most interesting part of the material?
I think the idea of zero-knowledge techniques is very fascinating. I think it is very cool that there is a scheme where one can identify oneself without revealing any part of the secret, and that the verifier can be satisfied.
Friday, November 9, 2012
12.1-12.2, due on 12 November
What was the most difficult part of the material for you?
Thinking about the (t,x)-threshold problem is a little interesting at first. I was also thoughtful about the Vandermonde matrix always being invertible.
What was the most interesting part of the material?
I think the idea of a shared secret is wonderfully interesting. I really enjoy how the schemes come together, and the practical implications for using such tools. This is a very interesting application of cryptography.
Thinking about the (t,x)-threshold problem is a little interesting at first. I was also thoughtful about the Vandermonde matrix always being invertible.
What was the most interesting part of the material?
I think the idea of a shared secret is wonderfully interesting. I really enjoy how the schemes come together, and the practical implications for using such tools. This is a very interesting application of cryptography.
Friday, November 2, 2012
9.1-9.4, due on November 5
What was the most difficult part of the material for you?
The most difficult part of the material was the section about the ElGamal signature scheme. There are more components of the signature than the RSA signature, and keeping track of all the pieces is more difficult.
What was the most interesting part of the material?
I think the idea of digitally signing documents is very interesting. I think it is a very cool idea to be able to prove that somebody has signed something. I think that this is a key part of the technology behind things like bitcoins.
The most difficult part of the material was the section about the ElGamal signature scheme. There are more components of the signature than the RSA signature, and keeping track of all the pieces is more difficult.
What was the most interesting part of the material?
I think the idea of digitally signing documents is very interesting. I think it is a very cool idea to be able to prove that somebody has signed something. I think that this is a key part of the technology behind things like bitcoins.
Thursday, November 1, 2012
8.4-8.5 and 8.7, due on November 2
What was the most difficult part of the material for you?
The most difficult part of the material was the section on multicollisions. It was difficult applying the birthday attack ideas to this idea.
What was the most interesting part of the material?
I think that birthday attacks are very interesting. It is a neat counter-intuitive problem. It once again shows why rigor is necessary along with intuition.
The most difficult part of the material was the section on multicollisions. It was difficult applying the birthday attack ideas to this idea.
What was the most interesting part of the material?
I think that birthday attacks are very interesting. It is a neat counter-intuitive problem. It once again shows why rigor is necessary along with intuition.
Friday, October 19, 2012
6.4.1-6.4.2 due on October 22
What was the most difficult part of the material for you?
In the Universal Exponent Factorization Method, there are a log of conditions and checks. Keeping track of all the conditions and checks is the most difficult part of the material.
What was the most interesting part of the material?
I think it is very interesting to see the linear algebra application in the Quadratic Sieve method of factorization. I think it is a clever way to do it, and I always enjoy seeing connections of linear algebra to number theory.
In the Universal Exponent Factorization Method, there are a log of conditions and checks. Keeping track of all the conditions and checks is the most difficult part of the material.
What was the most interesting part of the material?
I think it is very interesting to see the linear algebra application in the Quadratic Sieve method of factorization. I think it is a clever way to do it, and I always enjoy seeing connections of linear algebra to number theory.
Monday, October 15, 2012
6.3, due on October 17
What was the most difficult part of the material for you?
The Miller-Rabin Primality test was the most difficult part of the material for me. There were a lot of details as to why the test usually works. Following all these steps was difficult.
What was the most interesting part of the material?
I think it is very interesting that probabilistic methods are used in determining the primality of big numbers. It seems that RSA and other algorithms perhaps rely on these methods? If so then I wonder if there is anything exploitable with that. If not, then I guess that polynomial time deterministic algorithm is what is used in RSA implementations.
The Miller-Rabin Primality test was the most difficult part of the material for me. There were a lot of details as to why the test usually works. Following all these steps was difficult.
What was the most interesting part of the material?
I think it is very interesting that probabilistic methods are used in determining the primality of big numbers. It seems that RSA and other algorithms perhaps rely on these methods? If so then I wonder if there is anything exploitable with that. If not, then I guess that polynomial time deterministic algorithm is what is used in RSA implementations.
Friday, October 12, 2012
3.10, due on October 15
What was the most difficult part of the material for you?
As the book said, "it can be rather difficult to use by hand". Following all the by hand calculations was the most difficult part.
What was the most interesting part of the material?
I really like the new ideas of Lengendre and Jacobi symbols. I think that they have interesting properties, and there are some cool tricks you can do with them.
As the book said, "it can be rather difficult to use by hand". Following all the by hand calculations was the most difficult part.
What was the most interesting part of the material?
I really like the new ideas of Lengendre and Jacobi symbols. I think that they have interesting properties, and there are some cool tricks you can do with them.
Tuesday, October 9, 2012
6.2, due on October 10
What was the most difficult part of the material for you?
The section on "Low Exponent Attacks" had a lot of details. Keeping track of what everything means and how it all fits together was difficult.
What was the most interesting part of the material?
I thought the hardware timing attack was very interesting. It shows that math and computer application are not quite the same. You can have a perfect algorithm, but somewhere in the implementation there could be a flaw that dissolves the security.
The section on "Low Exponent Attacks" had a lot of details. Keeping track of what everything means and how it all fits together was difficult.
What was the most interesting part of the material?
I thought the hardware timing attack was very interesting. It shows that math and computer application are not quite the same. You can have a perfect algorithm, but somewhere in the implementation there could be a flaw that dissolves the security.
Friday, October 5, 2012
3.12, due on October 8
What was the most difficult part of the material for you?
Seeing the connection between the gcd and what was going on previously was intuitive, but hard to rigorously connect. It is a need connection though.
What was the most interesting part?
I think it is very interesting to be able to represent an arbitrary real number effectively in this way. It is cool that you can do better than just taking n decimal places over 10^n.
Seeing the connection between the gcd and what was going on previously was intuitive, but hard to rigorously connect. It is a need connection though.
What was the most interesting part?
I think it is very interesting to be able to represent an arbitrary real number effectively in this way. It is cool that you can do better than just taking n decimal places over 10^n.
Friday, September 28, 2012
3.5,3.6 due on October 1
What was the most difficult part of the material for you?
Keeping track of exactly what is going on in the Chinese remainder theorem is a little interesting. Lots of mods!
What was the most interesting part?
I really like the idea of modular exponentiation. I think it is cool that we can talk about what would be huge numbers, but which are manageable mod n.
Keeping track of exactly what is going on in the Chinese remainder theorem is a little interesting. Lots of mods!
What was the most interesting part?
I really like the idea of modular exponentiation. I think it is cool that we can talk about what would be huge numbers, but which are manageable mod n.
Thursday, September 27, 2012
Questions, due on September 28
Which topics and ideas do you think are the most important out of those we have studied?
I think that the knowledge of the purpose and uses of a cryptosystem, and the most common methods of attach, are the most important topics we have covered.
What kinds of questions do you expect to see on the exam?
I expect to see some of the basic results we have learned from number theory; definitions of certain ciphers; decrypting basic examples of ciphers; conceptual questions about various aspects of cryptography (methods of attack, etc.)
What do you need to work on understanding better before the exam?
I need to better memorize the specifics about the different ways to encrypt using a block cipher. I do not know how much of the DES/AES algorithms you want us to memorize, but if that is going to be tested extensively I would need to memorize those specifics as well.
I think that the knowledge of the purpose and uses of a cryptosystem, and the most common methods of attach, are the most important topics we have covered.
What kinds of questions do you expect to see on the exam?
I expect to see some of the basic results we have learned from number theory; definitions of certain ciphers; decrypting basic examples of ciphers; conceptual questions about various aspects of cryptography (methods of attack, etc.)
What do you need to work on understanding better before the exam?
I need to better memorize the specifics about the different ways to encrypt using a block cipher. I do not know how much of the DES/AES algorithms you want us to memorize, but if that is going to be tested extensively I would need to memorize those specifics as well.
Monday, September 24, 2012
5.1-5.4, due on September 26
What was the most difficult part of the material for you?
Keeping everything straight, especially in the encryption, was tiresome. There are no hard individual concepts, but keeping a bunch of little ideas strung together in the right way can be tricky.
What was the most interesting part of the material?
Learning how to pronounce "Rijndael"! Seriously, every time I would read it I would have a new crazy pronunciation attempt in my mind. I am glad to finally be enlightened.
Keeping everything straight, especially in the encryption, was tiresome. There are no hard individual concepts, but keeping a bunch of little ideas strung together in the right way can be tricky.
What was the most interesting part of the material?
Learning how to pronounce "Rijndael"! Seriously, every time I would read it I would have a new crazy pronunciation attempt in my mind. I am glad to finally be enlightened.
Saturday, September 22, 2012
Questions, due on September 24
How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?
I have spent typically 2 - 3 hours on homework assignments. The readings and lectures are very helpful in preparing for them.
What has contributed most to your learning in this class thus far?
No on element has been dominant in learning. An environment of reading, lecture, guided assignments, and self exploration have led to my learning thus far.
What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.)
I am not sure how much programming you want to be part of the class. I personally have usually built my own code to crack ciphers, rather than use the provided applets. I feel that this has been beneficial to me, and had I just used the applets I may not have understood the ciphers as well. However, this is not always feasible (ie the one time pad). And again, I am not sure how much programming you want to be required for the course.
Thursday, September 20, 2012
3.11, due on September 21
What was the most difficult part of the material for you?
This was a good review of 372 for me. It was a more in depth chapter than the previous. Some of the results were not immediately understandable.
What was the most interesting part?
I am excited to learn how AES used GF(2^8). I think it is going to be interesting to see.
This was a good review of 372 for me. It was a more in depth chapter than the previous. Some of the results were not immediately understandable.
What was the most interesting part?
I am excited to learn how AES used GF(2^8). I think it is going to be interesting to see.
Tuesday, September 18, 2012
4.5-4.8, due on September 18
What was the most difficult part of the material for you?
The notation for all the different bit shifts is new to me.
What was the most interesting part?
I liked learning about the history of DES.
The notation for all the different bit shifts is new to me.
What was the most interesting part?
I liked learning about the history of DES.
Wednesday, September 12, 2012
2.9-2.11, due on September 14
What was the most difficult part of the material for you?
The proofs regarding linear feedback shift registers were more intensive than we have previously seen. Remembering all the details might be a challenge.
What was the most interesting part?
I like how the one-time pad paradigm changes the question from generating a secure system to generating reproducible but high entropy sequences of random bits.
The proofs regarding linear feedback shift registers were more intensive than we have previously seen. Remembering all the details might be a challenge.
What was the most interesting part?
I like how the one-time pad paradigm changes the question from generating a secure system to generating reproducible but high entropy sequences of random bits.
Tuesday, September 11, 2012
3.8 and 2.5-2.8, due on September 12
What was the most difficult part of the material for you?
The German World War I cipher had some interesting steps. It took me a little while to understand why decryption works.
What was the most interesting part of the material?
I really like the concepts behind Hill's cipher. I enjoyed learning about the concepts of diffusion and confusion.
The German World War I cipher had some interesting steps. It took me a little while to understand why decryption works.
What was the most interesting part of the material?
I really like the concepts behind Hill's cipher. I enjoyed learning about the concepts of diffusion and confusion.
Saturday, September 8, 2012
2.3, due on September 10
What was the most difficult part of the material for you?
Understanding why the displacement revealed the key length.
What was the most interesting part of the material?
I loved the formulation of the code breaking as a linear algebra problem. I think it is a cool and elegant way to think about it. Plus, linear algebra operations have been optimized to death so the computation would be readily available.
Understanding why the displacement revealed the key length.
What was the most interesting part of the material?
I loved the formulation of the code breaking as a linear algebra problem. I think it is a cool and elegant way to think about it. Plus, linear algebra operations have been optimized to death so the computation would be readily available.
Wednesday, September 5, 2012
2.1-2.2 and 2.4, due on September 7
What was the most difficult part of the material for you?
Decrypting the affine cipher is interesting. I would need to remember the formulas in order to do so.
What was the most interesting part of the material?
I liked how the book outlined each of the four problems associated with breaking ciphers. It showed the various dangers of using different ciphers.
Decrypting the affine cipher is interesting. I would need to remember the formulas in order to do so.
What was the most interesting part of the material?
I liked how the book outlined each of the four problems associated with breaking ciphers. It showed the various dangers of using different ciphers.
Guest lecturer, due on September 7
What was the most difficult part of the material for you?
There was nothing terribly mathematical about the presentation. Reading the Deseret alphabet was difficult (impossible) for me.
What was the most interesting part of the material?
I find it very interesting how many different schemes were used. There were a lot of different things the early saints tried.
There was nothing terribly mathematical about the presentation. Reading the Deseret alphabet was difficult (impossible) for me.
What was the most interesting part of the material?
I find it very interesting how many different schemes were used. There were a lot of different things the early saints tried.
Thursday, August 30, 2012
3.2 3.3, due on August 31
What was the most difficult part of the material for you?
Working backwards through the Euclidean algorithm to find the explicit representation x,y satisfying ax + by = gcd(a,b) can be a little difficult to keep track of. I found it interesting that the book gave another possible algorithm.
What was the most interesting part of the material?
I enjoyed the introduction of fraction notation into modular arithmetic. I have not seen it before, but it makes a lot of sense and will help in simplifying notation.
Working backwards through the Euclidean algorithm to find the explicit representation x,y satisfying ax + by = gcd(a,b) can be a little difficult to keep track of. I found it interesting that the book gave another possible algorithm.
What was the most interesting part of the material?
I enjoyed the introduction of fraction notation into modular arithmetic. I have not seen it before, but it makes a lot of sense and will help in simplifying notation.
Tuesday, August 28, 2012
1.1-1.2 and 3.1, due on August 29
What was the most difficult part of the material for you?
Much of the basic number theory was review for me, though it is always good to refresh the mind on these essential proofs. Tracking each piece in the Euclidean algorithm can be difficult for me.
What was the most interesting part of the material?
I was happy to see the expansion from "there is no largest prime" to "there are about this many primes". I think the prime number theorem with its estimation formula will prove very useful in this class.
Much of the basic number theory was review for me, though it is always good to refresh the mind on these essential proofs. Tracking each piece in the Euclidean algorithm can be difficult for me.
What was the most interesting part of the material?
I was happy to see the expansion from "there is no largest prime" to "there are about this many primes". I think the prime number theorem with its estimation formula will prove very useful in this class.
Introduction, due on August 29
What is your year in school and major?
I am a junior studying Mathematics.
Which post-calculus math courses have you taken? (Use names or BYU course numbers.)
MATH 290, 313, 314, 334, 341, 342, 371, 372, 513R (IMPACT)
Why are you taking this class? (Be specific.)
I am taking this class for a few reasons. I have done and am doing much research with computation, so so cyber security is a big issue. As well, I have been wanting to learn a computer algebra system and this class will help me get hands on experience. Plus, cryptography seems like it will be a blast!
Do you have experience with Maple, Mathematica, SAGE, or another computer algebra system?
No.
Programming experience? How comfortable are you with using one of these programs to complete homework assignments?
Yes, a lot of Python experience; I am excited to learn SAGE.
Tell me about the math professor or teacher you have had who was the most and/or least effective. What did s/he do that worked so well/poorly?
I had a professor who was very clear in lecture, gave nice examples, explained the intuition, and answered questions clearly and with concern. I thought these were effective attributes.
Write something interesting or unique about yourself.
I am an avid fan of contemporary music.
If you are unable to come to my scheduled office hours, what times would work for you?
2pm any day of the week.
I am a junior studying Mathematics.
Which post-calculus math courses have you taken? (Use names or BYU course numbers.)
MATH 290, 313, 314, 334, 341, 342, 371, 372, 513R (IMPACT)
Why are you taking this class? (Be specific.)
I am taking this class for a few reasons. I have done and am doing much research with computation, so so cyber security is a big issue. As well, I have been wanting to learn a computer algebra system and this class will help me get hands on experience. Plus, cryptography seems like it will be a blast!
Do you have experience with Maple, Mathematica, SAGE, or another computer algebra system?
No.
Programming experience? How comfortable are you with using one of these programs to complete homework assignments?
Yes, a lot of Python experience; I am excited to learn SAGE.
Tell me about the math professor or teacher you have had who was the most and/or least effective. What did s/he do that worked so well/poorly?
I had a professor who was very clear in lecture, gave nice examples, explained the intuition, and answered questions clearly and with concern. I thought these were effective attributes.
Write something interesting or unique about yourself.
I am an avid fan of contemporary music.
If you are unable to come to my scheduled office hours, what times would work for you?
2pm any day of the week.
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