# Substitution–Permutation (SP) Network

**DOI:**https://doi.org/10.1007/0-387-23483-7_420

Shannon [1] suggested to use several mixing layers interleaving substitutions and permutations to build strong block ciphers. Such design is called a *substitution–permutation sandwich* or a substitution-permutation network (SPN). Although weak on its own, a line of *substitutions* followed by a *permutation* has good “mixing” properties: substitutions add to local *confusion* and permutation “glues” them together and spreads (*diffuses*) the local confusion to the more distant subblocks (see also substitutions and permutations). If one considers flipping a single bit at the input of such a network, it effects the *m* output bits of particular S-box which in turn are sent to different S-boxes by a permutation. Thus inputs/outputs of up to *m* S-boxes would be effected by the *avalanche*of change. These are again permuted into different S-boxes, covering almost all the S-boxes of the network. On the output of such network about half of the bits are effected by change and are flipped and about half of...

## References

- [1]Shannon, C.E. (1949). “Communication theory of secrecy system.”
*Bell System Technical Journal*, 28, 656–715.MathSciNetGoogle Scholar