A new family of ternary almost perfect nonlinear mappings
A mapping f(x) from GF(p(n)) to GF(p(n)) is differentially k-uniform if k is the maximum number of solutions x E GF(P") Of f(x + a) - f(x) = b, where a, b is an element of GF(P-n) and a not equal 0. A 2-uniform mapping is called almost perfect nonlinear (APN). This correspondence describes new families of ternary APN mappings over GF (3(n)), n >= 3 odd, of the form f(x) = ux(d)1 + x(d)2 where d(1) = 3(n)-1/2 -1 and d(2) = 3(n) - 2.
almost perfect nonlinear (apn) ternary mappings