3.4-3.5

1. I know I'm not supposed to say nothing, but this is the fourth time I've been "taught" the Chinese Remainder theorem and fourth I've gone over modular exponentiation.

2. Cryptography is a pretty good mix of the theoretical and the practical. On the one hand, secure cryptosystems need to be provably secure, and this almost always includes a mathematical analysis of the system in an idealized manner, as in, is it possible to break it without going through all possible solutions? Is there a method to obtain a solution analytically? On the other, we have real world needs of speed and convenience. We move from states to processes and algorithms, of which modular exponentiation is a prime example. Not only does it avoid overflow, the time complexity is logarithmic with the exponent and not linear like the naive, albeit correct, implementation is.