Differentially uniform mappings for cryptography

This work is motivated by the observation that in DES-like ciphers it is possible to choose the round functions in such a way that every non-trivial one-round characteristic has small probability. This gives rise to the following definition. A mapping is called differentially uniform if for every non-zero input difference and any output difference the number of possible inputs has a uniform upper bound. The examples of differentially uniform mappings provided in this paper have also other desirable cryptographic properties: large distance from affine functions, high nonlinear order and efficient computability.