A New Method of Construction of Permutation Trinomials with Coefficients 1

While big data technology is developing rapidly, it also brings numerous security and privacy issues, such as the security of communication between devices in Internet of Things and the confidentiality of stored data. The application of cryptography technology is the key to solving these problems. Permutation polynomials are widely utilized in both symmetric cryptography and public key cryptography. In recent years, the study of permutation polynomials with simple algebraic forms has attracted the interest of scholars. In this work, a novel approach for constructions of permutation trinomials with coefficients 1 is proposed by characterizing permutation polynomials with Niho-type exponents using the reverse method of Tu. In addition, for a three-term PP under a special case, this paper calculates its compositional inverse with explicit form.