Confusion and diffusion

In cryptography, confusion and diffusion are two properties of the operation of a secure cipher identified by Claude Shannon in his 1945 classified report A Mathematical Theory of Cryptography. These properties, when present, work to thwart the application of statistics and other methods of cryptanalysis.

These concepts are also important in the design of robust hash functions and pseudorandom number generators where decorrelation of the generated values is of paramount importance.

Confusion means that each binary digit (bit) of the ciphertext should depend on several parts of the key.

Diffusion means that if we change a single bit of the plaintext, then (statistically) half of the bits in the ciphertext should change, and similarly, if we change one bit of the ciphertext, then approximately one half of the plaintext bits should change.

Encryption is based on two principles: confusion and diffusion. Confusion means that the process drastically changes data from the input to the output. For example, by translating the data through a non-linear table created from the key. We have lots of ways to reverse linear calculations (starting with high school algebra), so the more non-linear it is, the more analysis tools it breaks.

Diffusion means that changing a single character of the input will change many characters of the output. Done well, every part of the input affects every part of the output, making analysis much harder. No confusion process is perfect: it always lets through some patterns. Good diffusion scatters those patterns widely through the output, and if there are several patterns making it through they scramble each other. This makes patterns vastly harder to spot, and vastly increases the amount of data to analyze to break the cipher.

The Advanced Encryption Standard (AES) has both excellent confusion and diffusion. Its confusion look-up tables are very non-linear and good at destroying patterns. Its diffusion stage spreads every part of the input to every part of the output: changing one bit of input changes half the output bits on average. Both confusion and diffusion are repeated several times for each input to increase the amount of scrambling. The secret key is mixed in at every stage so that an attacker cannot precalculate what the cipher does. None of this would happen if you used a simple one-stage scramble based on a key. Input patterns would flow straight through to the output. It might look random to the eye but analysis would find obvious patterns and the cipher could be broken.

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