Computer Security and Cryptography

9.10 DIFFERENTIAL CRYPTANALYSIS

Suppose two plaintexts are enciphered by S-box S[0] with the same key.

We conclude that

and write this last relationship as

where

How much of the 6-bit key is revealed by corresponding pairs of plain- and ciphertext (x_i, y_i) (i = 1, 2) enciphered by S-box S[0] with the same unknown key? That is, how many solutions are there to

given

Define

A pair (z₁, z₂) in (Δx, Δy) determines a possible unknown key by setting

If the size of (Δx, Δy) is much smaller ...