#### Dispersion and Diffusion

##### Samer Seraj

In Shannon's landmark 1949 paper Communication Theory of Secrecy Systems, the idea of diffusive functions is briefly mentioned. We consider two common definitions of such functions mapping between binary strings of fixed length. Given the dimension of the input space, we determine the minimum dimension of the output space for which such a function exists, by explicit construction and with respect to each definition. It will follow that each larger output dimension allows for such a function as well.

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