Answer to Question #200715 in Computer Networks for suma

Question

An avalanche effect is also desirable for the key: A one-bit change in a key should result in a dramatically different ciphertext if the plaintext is unchanged. 1. Assume an encryption with a given key. Now assume the key bit at position 1 (prior to PC − 1) is being flipped. Which S-boxes in which rounds are affected by the bit flip during DES encryption? 2. Which S-boxes in which DES rounds are affected by this bit flip during DES decryption?

Answer 1

1.

The key bit at position 1 is moved to position 8 by PC−1.

The two halves of the key which are independently rotated are referred to as C and D.

Since D₀ is all 0s, then D₁₋₁₆ will also be all 0s.

i.e. C₀ = 0100000₁₆ (due to the 1 in position 8).

In rounds 1, 2, 9, and 16, the key halves are rotated 1 position left and in all other rounds, they are rotated 2 positions to the left.

Note that, even after the PC−2 permutation, first-half key bits will remain in the first half and second-half key bits will remain in the second half after permutation respectively.

Thus we ignore about D when calculating which S-boxes are affected.

2.

The S-box 2.5 will be affected

At Round 16: 1-bit is occupying position 6

   After PC-2 this is sub key bit 10

   which affects S-box 2.5