CERTAIN CUBIC POLYNOMIALS OVER FINITE FIELDS

Title & Authors
CERTAIN CUBIC POLYNOMIALS OVER FINITE FIELDS
Kim, Hyung-Don; Kim, Jae-Moon; Yie, Ik-kwon;

Abstract
Motivated by XTR cryptosystem which is based on an irreducible polynomial $\small{x^3-cx^2+c^px-1}$ over $\small{F_{p^2}}$, we study polynomials of the form $\small{F(c,x)=x^3-cx^2+c^qx-1}$ over $\small{F_{p^2}}$ with $\small{q=p^m}$. In this paper, we establish a one to one correspondence between the set of such polynomials and a certain set of cubic polynomials over $\small{F_q}$. Our approach is rather theoretical and provides an efficient method to generate irreducible polynomials over $\small{F_{p^2}}$.
Keywords
irreducibility;normal basis;Hilbert Theorem 90;
Language
English
Cited by
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Korean Journal of Mathematics, 2011. vol.19. 3, pp.263-272
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