Explain in detail the round structure of DES Algorithm with proper representation.

The Data Encryption Standard (DES) is a symmetric-key block cipher published by the National Institute of Standards and Technology (NIST). DES is an implementation of a Feistel Cipher. It uses 16 round Feistel structure. The block size is 64-bit. Though, key length is 64-bit, DES has an effective key length of 56 bits, since 8 of the 64 bits of the key are not used by the encryption algorithm.

Here is a step-by-step explanation of the round structure of DES Algorithm:

1. Initial Permutation: The 64-bit plaintext goes through an initial permutation (IP) that rearranges the bits to produce the permuted input.

2. Dividing the Blocks: This permuted block is then divided into a left half (L0 of 32 bits) and a right half (R0 of 32 bits) for the process of the next round.

3. Expansion Permutation: The right half (32 bits) is expanded to 48 bits using the expansion permutation (E), denoted as E(R0).

4. Key Mixing: The result is then XORed with the round key Ki (48 bits) for that round.

5. Substitution: The 48-bit block obtained from the previous step is now subjected to 8 substitution boxes (S-boxes). Each S-box takes 6 bits as input and produces 4 bits as output. This results in a 32-bit output.

6. Permutation: The output from the S-boxes is then permuted using a fixed permutation table. This is the output of the round function, f.

7. XOR and Swap: This output is then XORed with the left half (L0) that we initially divided. The result of this XOR operation and the initial right half (R0) form the input for the next round.

8. Final Permutation: After 16 rounds, a final permutation (FP) is performed on the combined block (R16L16), to get the 64-bit ciphertext.

The representation of the round structure of DES Algorithm can be shown as follows:

L0, R0 = IP(plain text)
for i from 1 to 16
    L[i] = R[i-1]
    R[i] = L[i-1] XOR f(R[i-1], K[i])
end
cipher text = FP(R16L16)

Where:

• IP is the initial permutation
• FP is the final permutation
• f is the round function
• K[i] is the key for the i-th round
• L[i] and R[i] are the left and right halves of the block after the i-th round.