Sections 2.9-2.11 due September 17

1. (Difficult) I understood the proposition on Pg. 48, but the proof was difficult to follow. I understood the first part when it is shown that the det(M_n) = 0 for all n>N, but it was contradiction portion that I was getting confused. I also didn't understand how the period of a sequence is at most 2^m -1.

2. (Reflective) Using the bits for the key is something that I understand better now because the group we switched projects with used that as their cryptosystem. It is certainly an very good idea, because the key can be very long and hard to break. It makes sense that a one-time pad is unbreakable. The key is just as long as the plaintext, so really the only way to decrypt the message is with the key. Blum-Blum-Shub pseudo-random generator seemed like a good idea, but like it said it the book the numbers get large and it takes time to calculate. I had never thought about how important the randomness of the key would be, but it must be random or else someone could find a pattern or find a way to discover the key.