What was difficult?
Following the DES algorithm was very hard and something I will definitely have to pay attention to in class. All the numbers and diagrams and steps caused a lot of confusion with me when I tried to understand the cryptosystem.
Reflections
One of the cool things about cryptography that this chapter mentioned was using one system to send a key for another system. It just seems weird and cool at the same time that two different systems are used in tandem to send encrypted data (though it makes total sense).
Friday, May 30, 2008
Wednesday, May 28, 2008
Sec 9.1 - 9.4 due May 28th
What was difficult?
Following the algorithms were not all that hard. However, it is not easy to see what a "digital signature" is without actually seeing how it effects the document. At first I thought it was a little encoding appended to the end of the document (however as the book mentions) this would make it easy for an Eve to copy and past it anywhere she pleases. This would mean that the digital signature totally changes the actual message. It was hard for me to understand how one could get the message back, or how multiple people could sign a message. However, I am sure after going over the algorithms in class I will understand it.
Reflections
One of the things that was interesting was the mentioning of using the Birthday Attack to get someone to sign the hash of one document that had exactly the same hash of another document. It was interesting to see that it suggests changing the document before signing it which inhibits the birthday attack from succeeding. It seemed weird that such an attack can be thwarted by merely changing one character before signing.
Following the algorithms were not all that hard. However, it is not easy to see what a "digital signature" is without actually seeing how it effects the document. At first I thought it was a little encoding appended to the end of the document (however as the book mentions) this would make it easy for an Eve to copy and past it anywhere she pleases. This would mean that the digital signature totally changes the actual message. It was hard for me to understand how one could get the message back, or how multiple people could sign a message. However, I am sure after going over the algorithms in class I will understand it.
Reflections
One of the things that was interesting was the mentioning of using the Birthday Attack to get someone to sign the hash of one document that had exactly the same hash of another document. It was interesting to see that it suggests changing the document before signing it which inhibits the birthday attack from succeeding. It seemed weird that such an attack can be thwarted by merely changing one character before signing.
Friday, May 23, 2008
Sec 8.3 due May 23rd
What was difficult?
Understanding how SHA-1 works at all was very hard. It was difficult to make sense of the algorithm. I kind of was able to follow the steps, but it was very difficult to make sense of it all. I was hard to see what the algorithm was trying to accomplish mainly because it is an iterative algorithm and unless you use an example as you go it is hard to see what exactly is going on at each step.
Reflections
It is strange how much work is needed to come up with a secure hashing algorithm. It was also interesting to see how many times "good" hash functions are found out to actually be insecure. I have heard of both SHA and MD before as they are used a lot in computers for verification purposes. I believe they are also used to read computer virus signatures which programs like norton and sophos use to identify viral files.
Understanding how SHA-1 works at all was very hard. It was difficult to make sense of the algorithm. I kind of was able to follow the steps, but it was very difficult to make sense of it all. I was hard to see what the algorithm was trying to accomplish mainly because it is an iterative algorithm and unless you use an example as you go it is hard to see what exactly is going on at each step.
Reflections
It is strange how much work is needed to come up with a secure hashing algorithm. It was also interesting to see how many times "good" hash functions are found out to actually be insecure. I have heard of both SHA and MD before as they are used a lot in computers for verification purposes. I believe they are also used to read computer virus signatures which programs like norton and sophos use to identify viral files.
Monday, May 19, 2008
Questions due May 19th
Which topics do you think are most important out of those we’ve covered since the last midterm?
I think the most important topic since the first midterm is factoring and hash maps. I think learning and knowing how to apply the factoring algorithms given to us to try to break cryptosystems is important. Also, the idea of hash maps and there various uses is also important.
What kinds of questions do you expect to see on the midterm?
I expect to see questions asking to factor a certain integer using x method. Of course being there are no calculators the integer would have to be small and the method used would have to be able to be executed in a small amount of steps. I also see questions along the line of "is this a good hash map". Also, I forsee definition questions.
If you were writing a question that would be appropriate for the midterm, what would it be?
Here is xyz hash map function, is it strongly collision free?
Solve 7^x = 12 (mod 41) using Pohlig-Hellman
I think the most important topic since the first midterm is factoring and hash maps. I think learning and knowing how to apply the factoring algorithms given to us to try to break cryptosystems is important. Also, the idea of hash maps and there various uses is also important.
What kinds of questions do you expect to see on the midterm?
I expect to see questions asking to factor a certain integer using x method. Of course being there are no calculators the integer would have to be small and the method used would have to be able to be executed in a small amount of steps. I also see questions along the line of "is this a good hash map". Also, I forsee definition questions.
If you were writing a question that would be appropriate for the midterm, what would it be?
Here is xyz hash map function, is it strongly collision free?
Solve 7^x = 12 (mod 41) using Pohlig-Hellman
Friday, May 16, 2008
Sec 8.4 due May 16
What was hard?
Understanding the logic and math behind the birthday paradox was a bit hard. Not because I didnt understand it, but because it just seemed untrue (I guess that is why its a paradox). I also looked it up online to further prove to myself its true. Also, I dont really see the use of the birthday paradox, as the book points out BSGS algorithm is still somewhat superior and it will work all the time.
Reflections:
Even though the book didnt really make clear how the birthday attack is used to successfully attack a system, it still is a cool idea. I hope to see cool examples in the future of using the birthday attack to break a system (with high probability). Also, was nice seeing probability used, some of the calculations reminded me of poison distributions (which is what I think they were using to calculate some of the probabilities).
Understanding the logic and math behind the birthday paradox was a bit hard. Not because I didnt understand it, but because it just seemed untrue (I guess that is why its a paradox). I also looked it up online to further prove to myself its true. Also, I dont really see the use of the birthday paradox, as the book points out BSGS algorithm is still somewhat superior and it will work all the time.
Reflections:
Even though the book didnt really make clear how the birthday attack is used to successfully attack a system, it still is a cool idea. I hope to see cool examples in the future of using the birthday attack to break a system (with high probability). Also, was nice seeing probability used, some of the calculations reminded me of poison distributions (which is what I think they were using to calculate some of the probabilities).
Tuesday, May 13, 2008
Sec 8.1 - 8.2 due May 14
What was difficult
Due to my previous exposure to hashing algorithm the concept as a whole was easy to follow. following the explanation of the discrete log hash functions was hard, being that I am still a bit fuzzy with the whole idea of discrete logarithm.
Reflections
I have previous exposure to the use of hash algorithms for data signatures. At my job at Aerospace I worked in the Trusted Computer Systems lab. One of my focuses was learning about viruses and hacks as well as virus protection programs such as Sophos or Norton. The way virus detection works is via checking for signatures that match viral signatures. When you anti virus software does update on viruses it is updating its signature library to include recently discovered viruses. It is cool how you can check to see if something is a virus, much faster then looking through the whole document.
Due to my previous exposure to hashing algorithm the concept as a whole was easy to follow. following the explanation of the discrete log hash functions was hard, being that I am still a bit fuzzy with the whole idea of discrete logarithm.
Reflections
I have previous exposure to the use of hash algorithms for data signatures. At my job at Aerospace I worked in the Trusted Computer Systems lab. One of my focuses was learning about viruses and hacks as well as virus protection programs such as Sophos or Norton. The way virus detection works is via checking for signatures that match viral signatures. When you anti virus software does update on viruses it is updating its signature library to include recently discovered viruses. It is cool how you can check to see if something is a virus, much faster then looking through the whole document.
Sunday, May 11, 2008
Sec 7.3-7.5 due May 11th
What was difficult?
Following some of the math was again difficult. It is hard sometime to keep track of all the symbols and what not. The equation showing why ElGamal works took a couple reading thru to fully understand why tr^-a is equal to m (mod p). Also the section on security of ElGamal was a bit dense to read through. This reading was easy compared to previous readings on Discrete Logarithms tho.
Reflections:
The section on bit commitment was pretty cool. Implementing a way to show bob the predictions via one-way functions was interesting. The key exchange protocol mentioned in section 7.4 was also cool as you can use one idea to send the key securely, then use the key for another cryptosystem. Also the section on ElGamal Cryptosystem was good. Like RSA, I am amazed at how "hard" math problems can be used to give Eve all she really needs, yet, still have her be unable to decrypt messages.
Following some of the math was again difficult. It is hard sometime to keep track of all the symbols and what not. The equation showing why ElGamal works took a couple reading thru to fully understand why tr^-a is equal to m (mod p). Also the section on security of ElGamal was a bit dense to read through. This reading was easy compared to previous readings on Discrete Logarithms tho.
Reflections:
The section on bit commitment was pretty cool. Implementing a way to show bob the predictions via one-way functions was interesting. The key exchange protocol mentioned in section 7.4 was also cool as you can use one idea to send the key securely, then use the key for another cryptosystem. Also the section on ElGamal Cryptosystem was good. Like RSA, I am amazed at how "hard" math problems can be used to give Eve all she really needs, yet, still have her be unable to decrypt messages.
Thursday, May 8, 2008
7.1 and 7.2 due May 9th
What was difficult?
The difficult part (like usual) was keeping up with the math and notations. Following the Pohlig-Hellman Algorithm was hard and required several read throughs to follow. I also gave up on trying to understand the Baby Step, Giant Step section.
Reflections:
Like factoring, it amazes me that logarithms are hard to find in modular math. It just seems that if it is easy to do in regular math then it should be easy in modular math, however, this is not the case. It also seems interesting how just because the Pohlig-Hellman algorithm doesn't work for p=3(mod 4) it is hard (as far as we know) to calculate discrete logs.
The difficult part (like usual) was keeping up with the math and notations. Following the Pohlig-Hellman Algorithm was hard and required several read throughs to follow. I also gave up on trying to understand the Baby Step, Giant Step section.
Reflections:
Like factoring, it amazes me that logarithms are hard to find in modular math. It just seems that if it is easy to do in regular math then it should be easy in modular math, however, this is not the case. It also seems interesting how just because the Pohlig-Hellman algorithm doesn't work for p=3(mod 4) it is hard (as far as we know) to calculate discrete logs.
Tuesday, May 6, 2008
Sec 6.6 and 6.7 due May 7th
What is difficult?
Nothing was overall difficult about the reading. It was difficult understanding how such function exits such that f(x) is easy to compute but given y such that y = f(x) it is hard to find y. It seems like such a function would have to be so complex otherwise a binary search could easily find the x that will accomplish it.
Reflections:
As mentioned about the idea of trap door function is so new and weird to me. When I first learned RSA (and understood it) I was amazed at how you can use the fact that factoring is so complex. And it just perplexes me that there is no easy way to do these things. It was like when I learned about NP-hard and NP-complete problems. Just the idea of technically giving the enemy everything they need to know, yet they still cant decrypt seems so weird. And as computer and algorithm get faster and faster then perhaps the methods will fall and trap door functions will cease to exist!
Nothing was overall difficult about the reading. It was difficult understanding how such function exits such that f(x) is easy to compute but given y such that y = f(x) it is hard to find y. It seems like such a function would have to be so complex otherwise a binary search could easily find the x that will accomplish it.
Reflections:
As mentioned about the idea of trap door function is so new and weird to me. When I first learned RSA (and understood it) I was amazed at how you can use the fact that factoring is so complex. And it just perplexes me that there is no easy way to do these things. It was like when I learned about NP-hard and NP-complete problems. Just the idea of technically giving the enemy everything they need to know, yet they still cant decrypt seems so weird. And as computer and algorithm get faster and faster then perhaps the methods will fall and trap door functions will cease to exist!
Monday, May 5, 2008
Sec 6.5 due May 5th
What was difficult?
The section was short and sweet and nothing really difficult to understand about it. I dont really how they factored it using the idea of large primes and small primes. Or what the whole deal with the matrix was to try to factor n.
Reflections
I remember reading about the RSA challenge when I got a job as an intern in a trust systems lab. I remember downloading a program that would try to help factor problems in the RSA challenge during the computers down time as mentioned in the book. Its funny how it took 1600 computers 7 months to obtain a matrix and then another 57 hours to find the factors of n.
The section was short and sweet and nothing really difficult to understand about it. I dont really how they factored it using the idea of large primes and small primes. Or what the whole deal with the matrix was to try to factor n.
Reflections
I remember reading about the RSA challenge when I got a job as an intern in a trust systems lab. I remember downloading a program that would try to help factor problems in the RSA challenge during the computers down time as mentioned in the book. Its funny how it took 1600 computers 7 months to obtain a matrix and then another 57 hours to find the factors of n.
Friday, May 2, 2008
Sec 6.4 for May 2
What was difficult?
Following some of the factoring methods was a bit hard. I had to read over the p-1 factoring algorithm and the Quadratic Sieve a bunch of times before I understood what was going on. Its interesting to look at how factoring algorithms evolve as we try to get closer and closer to an efficient algorithm.
Reflection:
Though it was only a brief mention the text talked about the building of a quantum computer. I dont know much about quantum computers or what they even are, but every time I hear it mentioned it is doing something amazing. For example, a quantum computer can sort in O(n) time or efficiently factor. I really hope talk about quantum computers at one point in class. And if one is ever built things would go a lot faster!
Following some of the factoring methods was a bit hard. I had to read over the p-1 factoring algorithm and the Quadratic Sieve a bunch of times before I understood what was going on. Its interesting to look at how factoring algorithms evolve as we try to get closer and closer to an efficient algorithm.
Reflection:
Though it was only a brief mention the text talked about the building of a quantum computer. I dont know much about quantum computers or what they even are, but every time I hear it mentioned it is doing something amazing. For example, a quantum computer can sort in O(n) time or efficiently factor. I really hope talk about quantum computers at one point in class. And if one is ever built things would go a lot faster!
Subscribe to:
Posts (Atom)