Assignment 3:
1: Difficult: The most difficult part of the reading for sections 3.3, 2.1-2.2 was present accross all three sections, dealing with the multiplicative inverse for congruent values. Due to the increased reliance upon mathematics in cryptography, it has become common place to denote the letters of the alphabet numerically given values from 0-25 for each position. Thus, to change the plaintext values to ciphertext values it is necessary to have some knowledge of modular arithmetic to operate on the symbols. This was fairly straightforward and intuitive, but the operations using the multiplicative inverse and the conditions for using it required multiple reads to get the hang of. The inability to divide when the divisor and modular number (size of the ring) did not contain a gcd equal to one was also an interesting result of modular arithmetic that will still probably result in programming errors in the future. Overall, the modular arithmetic was intuitive and fairly easily understood, but these two issues, the multiplicative inverse and the lack of "closed under addition" were the hardest to grasp.

2. Overall the sections, including the necessary information on modular arithmetic, were a generous and easily understood introduction to some of the simplest ciphers in use even from ancient times such as the caeser cipher. These ciphers, while extremely simple in their mathematical application, were a good starting-off point to the understanding of the overall aim of cryptograhpy such as the treatment of plaintext and ciphertext. Unlike the original example in class, unfortunately, they also will present all ciphertext sans spaces which makes even the simplest cryptanalysis more realistic.