CERTAIN CUBIC POLYNOMIALS OVER FINITE FIELDS
Hyung-Don Kim, Jae Moon Kim, Ikkwon Yie · Journal of the Korean Mathematical Society · 2009
Motivated by XTR cryptosystem which is based on an irreducible polynomial $x^3-cx^2+c^px-1$ over $F_{p^2}$ , we study polynomials of the form $F(c,x)=x^3-cx^2+c^qx-1$ over $F_{p^2}$ with $q=p^m$ . In this paper, we establish a one to one correspondence between the set of such polynomials and a certain set of cubic polynomials over $F_q$ . Our approach is rather theoretical and provides an efficient method to generate irreducible polynomials over $F_{p^2}$ .