m-to-1 Mappings over Finite Fields 𝔽_q

Abstract

Permutation polynomials over finite fields have been widely studied due to their important applications in mathematics and cryptography. In recent years, 2-to-1 mappings over finite fields were proposed to build almost perfect nonlinear functions, bent functions, and the semi-bent functions. In this paper, we generalize the 2-to-1 mappings to m-to-1 mappings, including their construction methods. Some applications of m-to-1 mappings are also discussed.