APN permutations on ZnZn and Costas arrays

We study PN and APN functions over the integers modulo nn. We give some construction techniques based on Costas arrays, which allow us to construct APN permutations on Zp−1Zp−1 where pp is a prime. Although PN permutations do not exist, one set of our functions is very close to being a set of PN permutations.