Two generalizations of almost perfect nonlinearity

ePrint Report: Two generalizations of almost perfect nonlinearity

Claude Carlet

Almost perfect nonlinear (in brief, APN) functions are (so-called vectorial) functions $F: F_2^n\to F_2^n$ playing roles in several domains of information protection, at the intersection of computer science and mathematics. Their definition comes from cryptography and is also related to coding theory.
The cryptographic motivation for studying APN functions is that, when they are used as substitution boxes (S-boxes), ensuring nonlinearity in block ciphers, they contribute optimally to the resistance …

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