Suppose we define an encryption scheme as follows. The key will be four elements k1,k2,k3 and k4 in Z26 . The message space will be sequences of elements of of length 6. The ciphertext space will be the same as the message space.

The encryption algorithm is the following. Given a key and and a message , the corresponding ciphertext is , where:

b1 = k1a1 + k2a2 (mod 26)

b2 = k3a1 + k4a2 (mod 26)

b3 = k1a3 + k2a4 (mod 26)

b4 = k3a3 + k4a4 (mod 26)

b5 = k1a5 + k2a6 (mod 26)

b6 = k3a5 + k4a6 (mod 26)

Suppose that any four elements in Z₂₆ can be a key.

1. How many keys are there in the Hill Cipher described above?

2. Suppose we regard the Hill Cipher as described in the description as a block cipher. The blocks are elements of (i.e. sequences of letters of length 6). How many distinct blocks are there?