This problem provides a numerical example of encryption using a one-round version of DES. We start with the same bit pattern for both the key K and the plaintext block, namely:

Hexadecimal notation: 0 1 2 3 4 5 6 7 8 9 A B C D E F

Binary notation: 0000 0001 0010 0011 0100 0101 0110 0111

1000 1001 1010 1011 1100 1101 1110 1111

(Note: Please represent the result of each sub question using hexadecimal notation. Please also check the Appendix 1 in this document for the definitions of DES S-Boxes.)

1. Derive K₁, the first-round subkey.
2. Derive L₀, R₀.
3. Expand R₀ to get E[R₀], where E[] is the Expansion/permutation (E table) in DES.
4. Calculate A = E[R₀] K₁.
5. Group the 48-bit result of (d) into sets of 6 bits and evaluate the corresponding eight S-box substitutions.
6. Concatenate the results of (e) to get a 32-bit result, B.
7. Apply the permutation P to get P(B), where P() is the Permutation (P) table in DES.
8. Calculate R₁ = P(B) L₀ .
9. Write down the ciphertext.