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# Diffusion (cryptography)

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### Diffusion (cryptography)

In cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Claude Shannon in his paper Communication Theory of Secrecy Systems, published in 1949.

In Shannon's original definitions, confusion refers to making the relationship between the ciphertext and the symmetric key as complex and involved as possible; diffusion refers to making the relationship between the plaintext and the ciphertext as complex and involved as possible. This complexity is generally implemented through a well-defined and repeatable series of substitutions and permutations. Substitution refers the replacement of certain components (usually bits) with other components, following certain rules. Permutation refers to manipulation of the order of bits according to some algorithm. To be effective, any non-uniformity of plaintext bits needs to be redistributed across much larger structures in the ciphertext, making that non-uniformity much harder to detect.

In particular, for a randomly chosen input, if one flips the i-th bit, then the probability that the j-th output bit will change should be one half, for any i and jâ€”this is termed the strict avalanche criterion. More generally, one may require that flipping a fixed set of bits should change each output bit with probability one half.

One aim of confusion is to make it very hard to find the key even if one has a large number of plaintext-ciphertext pairs produced with the same key. Therefore, each bit of the ciphertext should depend on the entire key, and in different ways on different bits of the key. In particular, changing one bit of the key should change the ciphertext completely.

The simplest way to achieve both diffusion and confusion is to use a substitution-permutation network. In these systems, the plaintext and the key often have a very similar role in producing the output, hence the same mechanism ensures both diffusion and confusion.

## References

• Claude E. Shannon, "[1]
• Wade Trappe and Lawrence C. Washington, Introduction to Cryptography with Coding Theory. Second edition. Pearson Prentice Hall, 2006.
• William Stallings, Cryptography and Network Security, 3rd Edition, Prentice Hall, 2003
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