This work is supported in part by the National Natural Science Foundation of China (No.60172060), the Trans-Century Training Program Foundation for the Talents by the Education Ministry of China, and the Foundation for University Key Teacher by the Education Ministry of China.
We provide three techniques for constructing nonlinear zigzag functions from [GF(q)]^n to [GF(q)]^m. Taking use of permutations on [GF(q)]^m, we can construct new zigzag functions from old ones. This leads us to...