A New Family of Ternary Almost Perfect Nonlinear Mappings
Geir Jarle Ness, Tor Helleseth · IEEE Transactions on Information Theory · 2007
A mapping f(x) from GF(pn) to GF(pn) is differentially k-uniform if k is the maximum number of solutions x isin GF(pn) of f(x+a) - f(x) = b, where a, b isin GF(pn) and a ne 0. A 2-uniform mapping is called almost perfect nonlinear (APN). This correspondence describes new families of ternary APN mappings over GF(3n), n>3 odd, of the form f(x) = uxd+ xd2where d1= (3n-1)/2 - 1 and d2= 3n- 2.