Confusion and diffusion

In cryptography, confusion and diffusion are two properties of the operation of a secure cipher.

Confusion and diffusion were identified by Claude Elwood Shannon in his paper, "Communication Theory of Secrecy Systems" published in 1949. In Shannon's original definitions:

1. Confusion refers to making the relationship between the key and the ciphertext as complex and as involved as possible
2. Diffusion refers to the property that redundancy in the statistics of the plaintext is "dissipated" in the statistics of the ciphertext.

Diffusion is associated with the dependency of the output bits on the input bits. In a cipher with good diffusion, flipping an input bit should change each output bit with a probability of one half (this is termed the Strict Avalanche Criterion).

Substitution (a rule for replacing plaintext symbols by another) has been identified as a mechanism for primarily confusion (see S-box); on the other hand transposition using P-box (rearranging or swapping the order of symbols) is a technique for diffusion, although other mechanisms are also used in modern practice, such as linear transformations (e.g. in AES). Product ciphers use alternating substitution and transposition phases (rounds) to achieve both confusion and diffusion respectively.

Related pages

• Substitution-permutation network

References

• Claude E. Shannon, "Communication Theory of Secrecy Systems", Bell System Technical Journal, vol.28-4, page 656–715, 1949. [1] Archived 2007-06-05 at the Wayback Machine