CCZ-equivalence Of Two Classes Of APN Polynomials And APN Power Functions

Finding new(up to CCZ-equivalence)constructions of APN functions is one of the im?portant but difficult topics in the study of cryptographic functions.Up to now,there are 6infinite families of power APN functions and 14 families of APN pol_ynomials constructed.Although the CCZ-equivalence between power APN functions has been completely char?acterized,there is a lack of similar theoretical anal_ysis of the CCZ-equivalence between polynomial APN functions,and also a lack of theoretical analysis of the CCZ-equivalence between polynomial APN functions and power APN functions.This thesis gives the result that two families of pol_ynomial APN functions are CCZ-inequivalent to any power APN function.Moreover,the thesis prove the EA-equivalence between two APN functions.