The most difficult part of the reading was the explanation of the Quantum Fourier transform.
I had never thought about how superposition of states could be used as an effective tool in solving the problems of RSA (namely, factoring a large integer). However, it is an idea that correctly applied has the potential to work. Indeed, it has been shown that it can be solved provided a quantum computer. So the big obstacle here will just be actually building one, which could be a huge obstacle. Or maybe the government already has one and we just don't know it...
Sunday, November 18, 2012
Thursday, November 15, 2012
Section 19.1 and 19.2, due November 16
I had a little trouble understanding the explanation in the beginning about the polarity of particles and how that applies to sending messages through quantum cryptography.
The most interesting part of this section was definitely the mention of the possibility of factoring integers in polynomial time using an appropriate quantum computer. If this exists now, that could mean that RSA is totally open to anyone who has it. However, I have no idea what the actually likelihood is of the existence of a quantum computer is, or what a quantum computer is even, but I definitely want to know more.
The most interesting part of this section was definitely the mention of the possibility of factoring integers in polynomial time using an appropriate quantum computer. If this exists now, that could mean that RSA is totally open to anyone who has it. However, I have no idea what the actually likelihood is of the existence of a quantum computer is, or what a quantum computer is even, but I definitely want to know more.
Sunday, November 11, 2012
Sections 12.1 and 12.2, due November 12
The most difficult part of the reading was the part about the method to find the secret message using the of the message pairs and the Lagrange interpolating polynomial. An in class example will help a lot.
Secret splitting is a really interesting principle, and one that I had never really thought about. It can be implemented pretty simply and it would be infeasible to find the secret message without the correct amount of people. Also, I learned about Lagrange polynomials in my numerical methods not too long ago. I definitely didn't think there would be an interesting cryptographic application of Lagrange interpolation.
Secret splitting is a really interesting principle, and one that I had never really thought about. It can be implemented pretty simply and it would be infeasible to find the secret message without the correct amount of people. Also, I learned about Lagrange polynomials in my numerical methods not too long ago. I definitely didn't think there would be an interesting cryptographic application of Lagrange interpolation.
Tuesday, November 6, 2012
Section 8.3 and 9.5, due November 6
I think the most difficult part of the reading was the Secure Hash algorithm. A better explanation of it would be great.
I like the digital signature algorithm. It's simple to understand and a great application of RSA. It adds a deeper level of security to RSA and makes it that much more powerful.
I like the digital signature algorithm. It's simple to understand and a great application of RSA. It adds a deeper level of security to RSA and makes it that much more powerful.
Sunday, November 4, 2012
Section 9.1-9.4, due November 5
The most difficult part of the reading was the algorithm behind the ElGamal signature scheme and exactly how it uses discrete logarithms to generate signatures.
I really enjoyed the article about Zach Harris. It definitely helped me to understand the importance of digital signatures for emails. It also helped me to understand that internet security isn't perfect, and that people are always looking for ways around it, and sometimes a way around can be pretty simple and can be easily overlooked.
I really enjoyed the article about Zach Harris. It definitely helped me to understand the importance of digital signatures for emails. It also helped me to understand that internet security isn't perfect, and that people are always looking for ways around it, and sometimes a way around can be pretty simple and can be easily overlooked.
Dr. Chin Ling Guo, Math Biology Seminar, Extra Credit
On Thursday Nov. 1st I attended a Math Biology Seminar presented by Chin Ling Guo. It was about a project he's been doing in simulating the self-organization of epithelial tubules.
The most difficult aspect of the presentation was simply that the presenter had a more biological than mathematical background, so while the presentation was not terribly difficult to understand, some of the background explanations of the biology were a little difficult to understand.
The work that the presenter has been doing focuses on using mechanical cell-cell interactions in order to cause epithelial cells to self-organize into long tubules. Up until recently, many scientists have thought that causing this self-organization would require chemical cues, but by allowing cells to associate in the right type of extracellular matrix, mechanical associations allow the cells to self-organize properly.
The most difficult aspect of the presentation was simply that the presenter had a more biological than mathematical background, so while the presentation was not terribly difficult to understand, some of the background explanations of the biology were a little difficult to understand.
The work that the presenter has been doing focuses on using mechanical cell-cell interactions in order to cause epithelial cells to self-organize into long tubules. Up until recently, many scientists have thought that causing this self-organization would require chemical cues, but by allowing cells to associate in the right type of extracellular matrix, mechanical associations allow the cells to self-organize properly.
Tuesday, October 30, 2012
8.1-8.2, due October 31
I'm not sure I really understand what a collision is, or what a weakly collision-free hash function is. Also, I'm not sure I quite understand what the purpose of a hash function is.
Hash functions are a neat application of functions that are easy to evaluate, but difficult to invert, since we don't know what the preimage of the function is. Cryptography is built on some very simple principles, but all the same, they provide the necessary complexity for message security, or in this case to produce a digital signature for instance. With hash functions, the most simple properties of functions provide the basis for an important cryptographic implementation.
Hash functions are a neat application of functions that are easy to evaluate, but difficult to invert, since we don't know what the preimage of the function is. Cryptography is built on some very simple principles, but all the same, they provide the necessary complexity for message security, or in this case to produce a digital signature for instance. With hash functions, the most simple properties of functions provide the basis for an important cryptographic implementation.
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