Implement the stream cipher RC4 but use 16x4 bits instead of the full 256 bytes. That is, the state vector S is 16x4 bits. Assume that a plaintext of P = [3 5 4 6 9 11 13 12], and an 8x4-bit key of K = [1 3 5 7 9 11 13 15] are given.

Answer the following by demonstrating your work step by step:

1. Initialize the state vector S and temporary vector T.
2. Perform the initial permutation on S.
3. Generate the key stream.
4. Produce the ciphertext for the given plaintext P.