CERTAIN CUBIC POLYNOMIALS OVER FINITE FIELDS

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...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 46; no. 1; pp. 1 - 12
Main Authors Kim, Hyung-Don, Kim, Jae-Moon, Yie, Ik-kwon
Format Journal Article
LanguageKorean
Published 2009
Subjects
normal basis
irreducibility
Hilbert Theorem 90
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Summary: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 $F_{p^2}$.
Bibliography:KISTI1.1003/JNL.JAKO200907841290223
ISSN:0304-9914