Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Diffusion

The spreading of information across multiple bits in a cryptographic algorithm, enhancing security by making it harder to deduce information from a single bit.
📜

The statement of the theorem

Let E:{0,1}n×{0,1}k→{0,1}mE: \{0, 1\}^n \times \{0, 1\}^k \to \{0, 1\}^m be the cryptographic transformation, where MM is the plaintext and KK is the key. Diffusion requires that a small change in the input (plaintext or key) results in a large, unpredictable change in the output. Formally, for any two inputs (M,K)(M, K) and (M′,K′)(M', K') such that the Hamming distance H(M,M′)=1H(M, M') = 1 and H(K,K′)=0H(K, K') = 0, the output distance must be large:\nH(E(M,K),E(M′,K))≥m2−O(1)H(E(M, K), E(M', K)) \ge \frac{m}{2} - O(1) \n(Where H(⋅,⋅)H(\cdot, \cdot) is the Hamming distance and mm is the output length.)