J. Korean Math. Soc. 2009; 46(1): 1-12
Printed January 1, 2009
Copyright © The Korean Mathematical Society.
Hyung Don Kim, Jae Moon Kim, and Ikkwon Yie
Inha University, Inha University, Inha University
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 $F_{q^2}$ 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 $F_{q^2}$.
Keywords: irreducibility, normal basis, Hilbert Theorem 90
MSC numbers: 11T06, 11T55, 11T71
2017; 54(2): 517-543
2013; 50(6): 1213-1222
2004; 41(2): 309-318
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd