What was difficult?
All the sections were very hard to read through. As the book mentions it is hard to explain quantum computing to a non-physicists. I wasn't able to follow most of the chapter and a lot of the time I felt like I was just reading words rather then understanding anything. As a computer science major it was too much for me to except that a computer can do a lot of the things that they said it can do. And when it got into the math of Fourier transforms I got further confused.
Reflections
While I was not able to understand the bulk of the section I was able to get a few things out of it. Quantum computing has been brought up before to me and I have never understood it. I was told that quantum computers can also sort numbers in O(n) which is also amazing. Advance in technology are always amazing and I would love to see the ideas of quantum computing materialized. In all the section was interesting in the ideas it presented, though a lot of the math went right over my head
Friday, June 6, 2008
Monday, June 2, 2008
Sections 4.5-4.8 and 8.7 due June 2
What was hard?
Section 4.5 was very hard to follow. I guess I am easily scared when I see a bunch of symbols and diagrams. I was unable to follow most of the subsections and have a very loose understanding of the section as a whole. I am hoping that I will gain a better understanding of it from lecture.
Reflections:
Section 4.8 (on password security) was very interesting. One of the first things I learned about computer security is passwords. I was always told to use a alphanumeric password and to use a different password for all my accounts. Doing so would make it hard for my account to be broken into as well as make it so if one account is compromised...not all accounts become so. I found it interesting that there are ways to help safeguard people who choose somewhat dubious passwords with the addition of "salt".
Section 4.5 was very hard to follow. I guess I am easily scared when I see a bunch of symbols and diagrams. I was unable to follow most of the subsections and have a very loose understanding of the section as a whole. I am hoping that I will gain a better understanding of it from lecture.
Reflections:
Section 4.8 (on password security) was very interesting. One of the first things I learned about computer security is passwords. I was always told to use a alphanumeric password and to use a different password for all my accounts. Doing so would make it hard for my account to be broken into as well as make it so if one account is compromised...not all accounts become so. I found it interesting that there are ways to help safeguard people who choose somewhat dubious passwords with the addition of "salt".
Friday, May 30, 2008
Sections 4.1, 4.2, and 4.4 due May 30th
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).
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).
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!
Tuesday, April 29, 2008
Sec 2.12 due April 30th
What was difficult?
Understanding the internal workings of the engima was quite difficult. However, it really didnt matter how the innards of the machine worked because I was able to understand how the encryption process worked overall. It kind of seemed like a Vigenere cipher that just kept going. Also, understanding the part about permutations when it came to cracking the message key was a bit hard to fully follow.
Reflections
Whenever I tell someone I am taking an encryption class they always mention the Engima machine from World War II. Before, I never really knew much about the machine except from movies and such. However, now that I have read this section I fell like I can say something back to my friends, like about how to crack the machine or how it works.
Understanding the internal workings of the engima was quite difficult. However, it really didnt matter how the innards of the machine worked because I was able to understand how the encryption process worked overall. It kind of seemed like a Vigenere cipher that just kept going. Also, understanding the part about permutations when it came to cracking the message key was a bit hard to fully follow.
Reflections
Whenever I tell someone I am taking an encryption class they always mention the Engima machine from World War II. Before, I never really knew much about the machine except from movies and such. However, now that I have read this section I fell like I can say something back to my friends, like about how to crack the machine or how it works.
Sunday, April 27, 2008
Sec 6.3 due April 28th
What was Difficult?
The more difficult part about this section was following some of the primality tests. For example, I gave up trying to understand the Miller-Rabin Primality Test and also why it can fail sometimes. A lot of the justifications were also hard to follow. Its sometimes hard for me to read the really dry math explanations of how things work, I'm sure in class discussion (where I can ask questions) will help me better understand the material.
Reflections:
So up to this point all my primality testing functions that I have written in c code have been just try to divide the number by all the numbers up to its square root. Which always worked for me because I never really needed to test the primality of large numbers. However, as the book mentions this will take a computer 10^81 years to calculate all the primes under 10^10. So it was cool reading about all the improved methods of proving something prime or proving something to be composite.
The more difficult part about this section was following some of the primality tests. For example, I gave up trying to understand the Miller-Rabin Primality Test and also why it can fail sometimes. A lot of the justifications were also hard to follow. Its sometimes hard for me to read the really dry math explanations of how things work, I'm sure in class discussion (where I can ask questions) will help me better understand the material.
Reflections:
So up to this point all my primality testing functions that I have written in c code have been just try to divide the number by all the numbers up to its square root. Which always worked for me because I never really needed to test the primality of large numbers. However, as the book mentions this will take a computer 10^81 years to calculate all the primes under 10^10. So it was cool reading about all the improved methods of proving something prime or proving something to be composite.
Friday, April 25, 2008
What was difficult?
I found it hard to understand fully the section on Legendre and Jacobi Symbols. I kind of understand what they are, but once the math is shown I get totally lost in whats going on. Perhaps I am just getting lost in all the symbols. I'm pretty sure when backed with examples from class I will be on track.
Reflections:
Good old square roots are back. I find it amusing that like with regular math, square roots in modular math have more then one solution, however, they can also have more then two! It also seems like they are really tricky to calculate. I wonder if there will be a quadratic formula (my favorite formula) equivalent for modular math!
I found it hard to understand fully the section on Legendre and Jacobi Symbols. I kind of understand what they are, but once the math is shown I get totally lost in whats going on. Perhaps I am just getting lost in all the symbols. I'm pretty sure when backed with examples from class I will be on track.
Reflections:
Good old square roots are back. I find it amusing that like with regular math, square roots in modular math have more then one solution, however, they can also have more then two! It also seems like they are really tricky to calculate. I wonder if there will be a quadratic formula (my favorite formula) equivalent for modular math!
Sunday, April 20, 2008
Sec 6.2 due April 21st
What was difficult?
Keeping up with all the math was very difficult for this section. I had to read paragraphs over and over. There was a lot of complex math equations and description going on in this section regarding attacking RSA. I even gave up on some of the subsections and hope to learn the material in class on Monday.
Reflections
In CS 180 we learned about how to determine the efficiency of an algorithm. We even learned how some algorithms are not polynomial efficient and such. Reading this section kind of reminded me about that class as it went over ways of improving factoring algorithms given extra information about p,q or d. However, as mentioned above a lot of it was hard to follow.
Keeping up with all the math was very difficult for this section. I had to read paragraphs over and over. There was a lot of complex math equations and description going on in this section regarding attacking RSA. I even gave up on some of the subsections and hope to learn the material in class on Monday.
Reflections
In CS 180 we learned about how to determine the efficiency of an algorithm. We even learned how some algorithms are not polynomial efficient and such. Reading this section kind of reminded me about that class as it went over ways of improving factoring algorithms given extra information about p,q or d. However, as mentioned above a lot of it was hard to follow.
Friday, April 18, 2008
How long have you spent on the homework assignments?
I have spent a good 4-5 hours doing the homework assignments, the longest part is doing the ciphertext cracking.
Did lecture and the reading prepare you for them?
Yes
What have you liked/disliked about the class thus far?
Doing the math behind some of these "simple" cryptosystems is fun!
What do you think would help you learn more effectively or make the class better for you?
More real world similarity examples. Like when you talk about Alice and Bob sending boxes with locks on to each other really helps explain what the math behind it is trying to do
Are there topics you’re looking forward to learning about?
Public Key Algorithms
I have spent a good 4-5 hours doing the homework assignments, the longest part is doing the ciphertext cracking.
Did lecture and the reading prepare you for them?
Yes
What have you liked/disliked about the class thus far?
Doing the math behind some of these "simple" cryptosystems is fun!
What do you think would help you learn more effectively or make the class better for you?
More real world similarity examples. Like when you talk about Alice and Bob sending boxes with locks on to each other really helps explain what the math behind it is trying to do
Are there topics you’re looking forward to learning about?
Public Key Algorithms
Tuesday, April 15, 2008
Sec 3.7 and 6.1 due April 15th
What was difficult? and reflections
The most difficult part yet most interesting part of the reading was the section on RSA. It was hard to understand the underlying math of how RSA works mainly due to all the big scary numbers. It also bothers my that the "hardness" of factoring is the only thing that keeps this method secure. Eve has all the information she needs yet she has no way of solving for p and q, unless she makes very lucky guesses. It just seems strange and hard to grasp, the math side of me says it must be possible to factor while the computer scientist side of me says it cannot be done fast enough.
And that reason is why RSA also fascinates me. It is almost like giving your attacker everything they need but then taunt them for having the inability to solve for p and q. RSA was one of the first real encryption protocols I was taught back in my Aerospace job. So it is nice to have this refresher on it and to still be intrigued by it.
The most difficult part yet most interesting part of the reading was the section on RSA. It was hard to understand the underlying math of how RSA works mainly due to all the big scary numbers. It also bothers my that the "hardness" of factoring is the only thing that keeps this method secure. Eve has all the information she needs yet she has no way of solving for p and q, unless she makes very lucky guesses. It just seems strange and hard to grasp, the math side of me says it must be possible to factor while the computer scientist side of me says it cannot be done fast enough.
And that reason is why RSA also fascinates me. It is almost like giving your attacker everything they need but then taunt them for having the inability to solve for p and q. RSA was one of the first real encryption protocols I was taught back in my Aerospace job. So it is nice to have this refresher on it and to still be intrigued by it.
Sunday, April 13, 2008
Sections 3.4-3.6 due April 14th
What was difficult?
Understanding the sections on Fermat's Little Theorem and Euler's Theorem was a bit difficult. The proofs weren't easy to follow, however, I just tried it on enough test cases of my own to convince myself of their validity. The reading of the Three-Pass Protocol was also a little thick for me, so I hope to better understand it when it is mention in class.
Reflections
I found the brief section on modular exponentiation very fascinating. As a computer scientist it is many times in algorithmic designs I try to find shorter and less expense methods of computing something that would seem to take a long time. For example, many times a computer scientist has to look for polynomial time algorithms to solve problems in which brute force would be exponential time. So seeing the example of 2^1234 (mod 789) in which the largest number calculated is 788^2 was interesting.
Understanding the sections on Fermat's Little Theorem and Euler's Theorem was a bit difficult. The proofs weren't easy to follow, however, I just tried it on enough test cases of my own to convince myself of their validity. The reading of the Three-Pass Protocol was also a little thick for me, so I hope to better understand it when it is mention in class.
Reflections
I found the brief section on modular exponentiation very fascinating. As a computer scientist it is many times in algorithmic designs I try to find shorter and less expense methods of computing something that would seem to take a long time. For example, many times a computer scientist has to look for polynomial time algorithms to solve problems in which brute force would be exponential time. So seeing the example of 2^1234 (mod 789) in which the largest number calculated is 788^2 was interesting.
Thursday, April 10, 2008
2.9-2.11 due April 11th
What was difficult?
I found section 2.11 to be the most difficult to read through of all the sections thus far. The material wasn't really straight forward and easy to assimilate. Also, the proofs were a bit thick. I had to read through the examples a couple of times to understand what the meaning of the matrices were and what they were actually trying to solve. I am still a bit fuzzy on some of the stuff and hopefully it will be cleared up in class.
Reflections
I really liked the section about Pseudo-Random Bit Generation. As a computer science major, I use random numbers all the time as well as come up with system to create random numbers using hardware. It was interesting to read about how the random number generators I usually work with are in fact not cryptographically secure. It seemed weird to me that it is possible for people to predict the next numbers in the "random" sequence. It was also cool seeing the methods proposed by the book that are cryptographically secure.
I found section 2.11 to be the most difficult to read through of all the sections thus far. The material wasn't really straight forward and easy to assimilate. Also, the proofs were a bit thick. I had to read through the examples a couple of times to understand what the meaning of the matrices were and what they were actually trying to solve. I am still a bit fuzzy on some of the stuff and hopefully it will be cleared up in class.
Reflections
I really liked the section about Pseudo-Random Bit Generation. As a computer science major, I use random numbers all the time as well as come up with system to create random numbers using hardware. It was interesting to read about how the random number generators I usually work with are in fact not cryptographically secure. It seemed weird to me that it is possible for people to predict the next numbers in the "random" sequence. It was also cool seeing the methods proposed by the book that are cryptographically secure.
Tuesday, April 8, 2008
2.5-2.8 due April 9th
What was difficult?
Following the encryptions methods and decryption methods (and verifying that they work) was a little difficult for me. Specifically when it came to doing the Hill ciphers where matrix multiplication was being done mod 26. Took some time to convince myself that you can use the mod 26 version of the inverse rather then the true mathematical inverse to decrypt.
Reflections
It really impresses me the cleverness and creativity that goes into some of these ciphers. I like how we are getting into more complex ciphers and its just very interesting what some people came up with. I really liked the Hill cipher as I thought it was a really cool idea to use matrices to encrypt blocks of letters instead of just one at a time.
Following the encryptions methods and decryption methods (and verifying that they work) was a little difficult for me. Specifically when it came to doing the Hill ciphers where matrix multiplication was being done mod 26. Took some time to convince myself that you can use the mod 26 version of the inverse rather then the true mathematical inverse to decrypt.
Reflections
It really impresses me the cleverness and creativity that goes into some of these ciphers. I like how we are getting into more complex ciphers and its just very interesting what some people came up with. I really liked the Hill cipher as I thought it was a really cool idea to use matrices to encrypt blocks of letters instead of just one at a time.
Sunday, April 6, 2008
2.3-2.4 due April 7th
What was the most difficult part of the material for you?
The material was mostly straight forward and simple to understand. I am, however, skeptical of the frequency chart methods to crack the codes. It just seems very hand-wavish the way they are able to "guess" the correct corresponding letters via the simple analysis. Of course, they did mention it is very hard to skew the message letter frequencies. After looking at the math of it I guess it made more sense.
Reflections
Like last reading, it was again cool to see the basic cryptosystems I used to play around with as a kid developed in a mathematical sense. The dot products with the frequency vectors did seem like a very clever trick to crack such systems and I enjoyed reading these sections. Of course the math just helps you get a head start, after which, it is back to the guesswork of the childish puzzles!
The material was mostly straight forward and simple to understand. I am, however, skeptical of the frequency chart methods to crack the codes. It just seems very hand-wavish the way they are able to "guess" the correct corresponding letters via the simple analysis. Of course, they did mention it is very hard to skew the message letter frequencies. After looking at the math of it I guess it made more sense.
Reflections
Like last reading, it was again cool to see the basic cryptosystems I used to play around with as a kid developed in a mathematical sense. The dot products with the frequency vectors did seem like a very clever trick to crack such systems and I enjoyed reading these sections. Of course the math just helps you get a head start, after which, it is back to the guesswork of the childish puzzles!
Thursday, April 3, 2008
Sec 3.3 and 2.1-2.2 due April 4th
What was the most difficult part of the material for you?
By far the most challenging aspect of the readings was learning about modular arithmetic. I found myself re-reading and doing practice examples until I was able to convince my self of some of the properties. Specifically, when it got to the section on fractions I was having a hard time following. I guess it took me a while to allow me to accept that 1/2 = 6173 in (mod 12345).
Reflections:
I really enjoyed reading the section on shift and affine ciphers. It brought me back to the days of decoder rings in cereal boxes. It was just interesting to see it presented so formally and mathematically as done in these sections. As a kid I would just search every possible key-space but now I have more tools to crack these codes!
I eagerly await the introduction and breaking of my sophisticated cryptosystems.
By far the most challenging aspect of the readings was learning about modular arithmetic. I found myself re-reading and doing practice examples until I was able to convince my self of some of the properties. Specifically, when it got to the section on fractions I was having a hard time following. I guess it took me a while to allow me to accept that 1/2 = 6173 in (mod 12345).
Reflections:
I really enjoyed reading the section on shift and affine ciphers. It brought me back to the days of decoder rings in cereal boxes. It was just interesting to see it presented so formally and mathematically as done in these sections. As a kid I would just search every possible key-space but now I have more tools to crack these codes!
I eagerly await the introduction and breaking of my sophisticated cryptosystems.
Tuesday, April 1, 2008
1.1-1.2, 3.1-3.2, due on April 2.
What was the most difficult part of the material for you?
Most puzzling to me in sections 1.1 and 1.2 was the idea of a key and how it is used. I get the real life analogy of keys for locks, however, I found myself wondering a lot how is the key used in terms of computers. For now I just see it as this magical number that does something according to the algorithms.
The proofs in section 3.1 pertaining to the prime numbers were hard to follow. However, I intuitively understood why the corollaries were true so it wasn't a big deal.
Also, 3.2 took a while to understand it took a few reads through to even understand what was going on
Reflections:
A lot of introduction information was given in this first readings. I am most interested in seeing and learning the algorithm, specifically, the public key algorithms that solve the problems that can arise in cryptology. I have had some exposure to cryptographic methods and number theory so a lot of this was a refresher on what cryptology accomplishes.
Also, it seems that prime numbers will be useful in the course which is cool cause I really like number theory surrounding prime numbers. Perhaps my favorite proof, though not mentioned in the book, is the proof that there are infinite prime numbers.
Most puzzling to me in sections 1.1 and 1.2 was the idea of a key and how it is used. I get the real life analogy of keys for locks, however, I found myself wondering a lot how is the key used in terms of computers. For now I just see it as this magical number that does something according to the algorithms.
The proofs in section 3.1 pertaining to the prime numbers were hard to follow. However, I intuitively understood why the corollaries were true so it wasn't a big deal.
Also, 3.2 took a while to understand it took a few reads through to even understand what was going on
Reflections:
A lot of introduction information was given in this first readings. I am most interested in seeing and learning the algorithm, specifically, the public key algorithms that solve the problems that can arise in cryptology. I have had some exposure to cryptographic methods and number theory so a lot of this was a refresher on what cryptology accomplishes.
Also, it seems that prime numbers will be useful in the course which is cool cause I really like number theory surrounding prime numbers. Perhaps my favorite proof, though not mentioned in the book, is the proof that there are infinite prime numbers.
Monday, March 31, 2008
Introduction, due on April 2
What is your year in school and major? Senior (4th year), Computer Science
What post-calculus math course have you taken? Math Modeling, Combinatorics, Mathematical Game Theory, Linear Algebra
Why are you taking this class? Interest in cryptology and using it to complete math minor.
Programming Experience: I know how to program in Mathematica and I am sure I could pick up the other programs easily. I feel comfortable with using any of the languages listed.
Most Effective Teachers: Do not just quote the book verbatim but rather expand on topics learned from the book. I had math teachers that basically go line by line what the book says, which taught me nothing more than I would get from reading the book.
Something interesting/unique about me: Used to play tournament chess with a chess coach and all.
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