Difficult:
I would like to go through some examples of using the elliptic curve cryptosystem. It seems that we can use elliptic curve to improve most cryptosystems that use discrete logs and some that don't. I'm not really sure how it improves each cryptosystem except that it makes the discrete logarithm harder to find.
Reflective:
I think it's interesting that the elliptic curve cryptosystem essentially builds off the other cyrptosystems. I was wondering if there is any stand alone elliptic curve method or if it always requires some base system to improve. Also I was curious how we can use the elliptic curve to improve non discrete log cryptosystems.
I also completed the student ratings for this course.
Monday, November 25, 2013
16.4, due December 9
Difficult:
I think I understand the reasons of why we need to modify the elliptic curves mod 2. I'm not really sure what we are doing when we modify them and what makes the modified curve more secure than the original cure mod 2. I think I would like to see a geometric representation of what is happening and why that is better.
Reflective:
I think it is interesting that the NIST recommended elliptic curves for cryptographic use. It always makes me wonder what they have in mind as the give suggestions. I know in some cases such as DES they made it more secure. But with elliptic curves I wonder if they knew that people would need to modify the elliptic curves in order to make them secure for use.
I think I understand the reasons of why we need to modify the elliptic curves mod 2. I'm not really sure what we are doing when we modify them and what makes the modified curve more secure than the original cure mod 2. I think I would like to see a geometric representation of what is happening and why that is better.
Reflective:
I think it is interesting that the NIST recommended elliptic curves for cryptographic use. It always makes me wonder what they have in mind as the give suggestions. I know in some cases such as DES they made it more secure. But with elliptic curves I wonder if they knew that people would need to modify the elliptic curves in order to make them secure for use.
16.3, due December 6
Difficult:
I think I understand the basic idea behind factoring with elliptic curves. Essentially the two primes p and q that compose n behave differently and thus we can find pa and q. I had a difficult time following the examples so I think an in class example would be very helpful.
Reflective:
I was wondering how the elliptic curve method of factoring compares with other methods of factoring. It seems like it can be much quicker in some cases. However, it also seems that as long as we choose good large primes we can still be fairly sure that n won't be factored. I was wondering how much better the method is and also if it is more versatile.
I think I understand the basic idea behind factoring with elliptic curves. Essentially the two primes p and q that compose n behave differently and thus we can find pa and q. I had a difficult time following the examples so I think an in class example would be very helpful.
Reflective:
I was wondering how the elliptic curve method of factoring compares with other methods of factoring. It seems like it can be much quicker in some cases. However, it also seems that as long as we choose good large primes we can still be fairly sure that n won't be factored. I was wondering how much better the method is and also if it is more versatile.
16.2, due December 4
Difficult:
I don't understand representing plaintext with the curve. I get the idea of needing to match the message to a point on the curve and then using elliptic curve operations on that point to obtain a ciphertext. What I don't understand is both what elliptic curve operations are done and also I didn't understand how the message is mapped to a point on the curve originally.
Reflective:
The elliptic curve method reminds me a lot of shamir secret sharing since both involve a linear equation and finding points on that line. It does seem especially important that it is extremely important to choose primes because if not we can easily factor the number.
I don't understand representing plaintext with the curve. I get the idea of needing to match the message to a point on the curve and then using elliptic curve operations on that point to obtain a ciphertext. What I don't understand is both what elliptic curve operations are done and also I didn't understand how the message is mapped to a point on the curve originally.
Reflective:
The elliptic curve method reminds me a lot of shamir secret sharing since both involve a linear equation and finding points on that line. It does seem especially important that it is extremely important to choose primes because if not we can easily factor the number.
Monday, November 18, 2013
16.1, due December 2
Difficult:
So I think I understand the basics of elliptic curves and the addition rule seems fairly straight forward. It is interesting that from any two points you can generate a third just base on those points. I'm not sure how this is actually used in a crytpo system but we'll probably get to that in the next section.
Reflective:
It is impressive that we can drastically reduce our key size when using the elliptic curve method. I was wondering if elliptic curves can be used in both public key cryptography and symmetric key. I'm not sure if we really need to use it for both but I also haven't seen the actual encryption method.
So I think I understand the basics of elliptic curves and the addition rule seems fairly straight forward. It is interesting that from any two points you can generate a third just base on those points. I'm not sure how this is actually used in a crytpo system but we'll probably get to that in the next section.
Reflective:
It is impressive that we can drastically reduce our key size when using the elliptic curve method. I was wondering if elliptic curves can be used in both public key cryptography and symmetric key. I'm not sure if we really need to use it for both but I also haven't seen the actual encryption method.
18.1 and 18.2, due November 26
Difficult:
I had a difficult time understanding the error correcting codes. I think I basically understood all the examples that were in the introduction about how we can check for errors, but I got lost in section 18.2. I understood the Hamming distance but I'm not sure how we really get the codewords or how we use the codewords once we have them.
Reflective:
It seems that error checking often involves either resending information or just sending multiple repetitions of the same message. It seems that this could get expensive very quickly, especially for large messages. I'm not sure if there is a better way but it does seem that there could be a pretty large cost with error checking.
I had a difficult time understanding the error correcting codes. I think I basically understood all the examples that were in the introduction about how we can check for errors, but I got lost in section 18.2. I understood the Hamming distance but I'm not sure how we really get the codewords or how we use the codewords once we have them.
Reflective:
It seems that error checking often involves either resending information or just sending multiple repetitions of the same message. It seems that this could get expensive very quickly, especially for large messages. I'm not sure if there is a better way but it does seem that there could be a pretty large cost with error checking.
2.13, due November 25
Difficult:
It seems like the enigma machine itself would be somewhat secure. I do question needing a codebook to set the rotors everyday because it seems that if the codebook was captured it would be very easy to decrypt messages and also send false messages. I don't think I fully understood the basics of how they were able to crack the enigma machine. That might just be because my permutation knowledge is a bit rusty.
Reflective:
I think that creating a machine to encrypt and decrypt messages is a very smart idea especially in war. This way the knowledge of even how the cipher worked would be more hidden because the operators may not even know how the machine works and thus if they are captured they can break the machine and no one knows how to decrypt the messages.
It seems like the enigma machine itself would be somewhat secure. I do question needing a codebook to set the rotors everyday because it seems that if the codebook was captured it would be very easy to decrypt messages and also send false messages. I don't think I fully understood the basics of how they were able to crack the enigma machine. That might just be because my permutation knowledge is a bit rusty.
Reflective:
I think that creating a machine to encrypt and decrypt messages is a very smart idea especially in war. This way the knowledge of even how the cipher worked would be more hidden because the operators may not even know how the machine works and thus if they are captured they can break the machine and no one knows how to decrypt the messages.
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