New families of almost perfect nonlinear power mappings
Tor Helleseth, Chunming Rong, Daniel Sandberg · IEEE Transactions on Information Theory · 1999
A power mapping f(x)=x/sup d/ over GF(p/sup n/) is said to be differentially k-uniform if k is the maximum number of solutions x/spl isin/GF(p/sup n/) of f(x+a)-f(x)=b where a, b/spl isin/GF(p/sup n/) and a/spl ne/0. A 2-uniform mapping is called almost perfect nonlinear (APN). We construct several new infinite families of nonbinary APN power mappings.