Question 2:
a) Shift cipher: Same plaintext characters are encrypted to same
ciphertext charaters. So Eve will get a ciphertext which consists of 1
character repeating many times. For each key, Eve will get a corresponding
plaintext which consists of 1 character repeating many times. Because the
plaintext is meaningless and the probability that Alice chose a specific
character is equally likely for 26 characters, Eve cannot deduce the key.
b) Affine cipher: Same plaintext characters are encrypted to same
ciphertext characters. So it is similar to part a, Eve cannot deduce the
key
c) Vigenere cipher: Vigenere cipher is symmetric, so encrypting 1
character repeating many times with a key equals to encrypting this key
repeating many times with the key which is only 1 character. This is
equivalent to encrypting the key which Alice used using shift cipher.
Since the key is of length 8 to 12 characters, it is very likely that a
ciphertext can only map to one meaningful plaintext. So Eve can try an
exhaustive search to obtain the key which Alice used.

Question 4:
a) 101 = 5 x 17 + 16 and 17 = 1 x 16 + 1 so
    17 = 1 x (101 - 5 x 17) + 1
    -101 + 6 x 17 = 1
    Therefore, x = 6 and y = -1 so that 17x + 101y = 1
b) Since 6 x 17 - 101 = 1 mod 101, so 6 x 17 = 1 mod 101. Therefore the
inverse of 17 mod 101 is 6.