## Cryptology ePrint Archive: Report 2009/053

New commutative semifields defined by PN multinomials

Lilya Budaghyan and Tor Helleseth

Abstract: We introduce infinite families of perfect nonlinear Dembowski-Ostrom multinomials over \$F_{p^{2k}}\$ where \$p\$ is any odd prime. We prove that for \$k\$ odd and \$p\ne3\$ these PN functions define new commutative semifields (in part by studying the nuclei of these semifields). This implies that these functions are CCZ-inequivalent to all previously known PN mappings.

Category / Keywords: foundations / Commutative semifield, Equivalence of functions, Perfect nonlinear, Planar function

Publication Info: Part of this work was presented at SETA'08