Bivariate functions with low c-differential uniformity

Starting with the multiplication of elements in Fq2 which is consistent with that over Fq2, where q is a prime power, via some identification of the two environments, we investigate the c-differential uniformity for bivariate functions F(x,y)=(G(x,y),H(x,y)). By carefully choosing the functions G(x,y) and H(x,y), we present several constructions of bivariate functions with low c-differential uniformity, in particular, many PcN and APcN functions can be produced from our constructions.