3. Let X' denote the bit-by-bit complement of a bit string X a. Show that if C-DESK(M), then C DESK(M'). (Go through each step of DES and tell which intermediate values are complemented and which are not. For example, is the input to the third S-box in Round 5 complemented when M and K are replaced by their complements? Explain why your answers are correct.) b. Explain how this property can be exploited in a chosen-plaintext attack to reduce the search effort by roughly 50%. Part of your answer should be an algorithm which tells exactly what to do. (Hint: Begin by obtaining the ciphertext for a plaintext M and for its complement M-) 3. Let X' denote the bit-by-bit complement of a bit string X a. Show that if C-DESK(M), then C DESK(M'). (Go through each step of DES and tell which intermediate values are complemented and which are not. For example, is the input to the third S-box in Round 5 complemented when M and K are replaced by their complements? Explain why your answers are correct.) b. Explain how this property can be exploited in a chosen-plaintext attack to reduce the search effort by roughly 50%. Part of your answer should be an algorithm which tells exactly what to do. (Hint: Begin by obtaining the ciphertext for a plaintext M and for its complement M-)