TY - GEN

T1 - A relation between self-reciprocal transformation and normal basis over odd characteristic field

AU - Kobayashi, Shigeki

AU - Nogami, Yasuyuki

AU - Sugimura, Tatsuo

PY - 2009/12/1

Y1 - 2009/12/1

N2 - Let q and f(x) be an odd characteristic and an irreducible polynomial of degree m over Fq, respectively. Then, suppose that F(x) = x m f(x+x-1) is irreducible over Fq. This paper shows that the conjugate zeros of F(x) with respect to Fq form a normal basis in Fq2m if and only if those of f(x) form a normal basis in Fqm and the partial conjugates given as follows are linearly independent over Fq, {γ - γ-1, (γ - γ-1)q, · · · , (γ - γ-1)qm-1}, (1) where γ is a zero of F(x) and thus a proper element in Fq2m. In addition, from the viewpoint of q-polynomial, this paper proposes an efficient method for checking whether or not the conjugate zeros of F(x) satisfy the condition.

AB - Let q and f(x) be an odd characteristic and an irreducible polynomial of degree m over Fq, respectively. Then, suppose that F(x) = x m f(x+x-1) is irreducible over Fq. This paper shows that the conjugate zeros of F(x) with respect to Fq form a normal basis in Fq2m if and only if those of f(x) form a normal basis in Fqm and the partial conjugates given as follows are linearly independent over Fq, {γ - γ-1, (γ - γ-1)q, · · · , (γ - γ-1)qm-1}, (1) where γ is a zero of F(x) and thus a proper element in Fq2m. In addition, from the viewpoint of q-polynomial, this paper proposes an efficient method for checking whether or not the conjugate zeros of F(x) satisfy the condition.

KW - Normal basis

KW - Polynomial transformation

KW - Self-reciprocal irreducible polynomial

UR - http://www.scopus.com/inward/record.url?scp=77749277591&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77749277591&partnerID=8YFLogxK

U2 - 10.1109/ICCIT.2009.119

DO - 10.1109/ICCIT.2009.119

M3 - Conference contribution

AN - SCOPUS:77749277591

SN - 9780769538969

T3 - ICCIT 2009 - 4th International Conference on Computer Sciences and Convergence Information Technology

SP - 999

EP - 1004

BT - ICCIT 2009 - 4th International Conference on Computer Sciences and Convergence Information Technology

T2 - 4th International Conference on Computer Sciences and Convergence Information Technology, ICCIT 2009

Y2 - 24 November 2009 through 26 November 2009

ER -