The differential uniformity of the power functions xpn+5/2 over Fpn

Cryptographic functions with low differential uniformity have important applications in designing S-box in the block ciphers. In this paper, we mainly investigate the differential uniformity Delta(F) on a new class of power mappings F(x)= x(pn+ 5/2) over F-pn with p being an odd prime and n being a positive integer. More precisely, for p= 3, the differential uniformity and the differential spectrum of F have been determined explicitly. The results indicate that F is a locally-PN function with differentially 3n+1/4-uniform when nis odd and a locally-APN function with differentially 3n+3/4-uniform when n is even. Then, for p= 5, we prove that F is APN for even nand Delta(F)= 6 for odd nthrough specific differential equations and quadratic character over F-5n. The method is different from the