TY - GEN

T1 - Systematic generation of an irreducible polynomial of an arbitrary degree m over double struck F signp such That p > m

AU - Nasu, Hiroaki

AU - Nogami, Yasuyuki

AU - Morikawa, Yoshitaka

AU - Kobayashi, Shigeki

AU - Sugimura, Tatsuo

PY - 2008/12/31

Y1 - 2008/12/31

N2 - This paper proposes a method for generating an irreducible polynomial of an arbitrary degree m over an arbitrary prime field double struck F sign p such that p > m. The proposed method is closely related to the minimal polynomial determination and therefore it has the following features: its complexity has little dependency on the size of characteristic p, its calculation cost is explicitly given with degree m, and it can generate primitive polynomials when pm - 1 is factorized as the product of prime numbers. The restriction p > m comes from using Newton's formula.

AB - This paper proposes a method for generating an irreducible polynomial of an arbitrary degree m over an arbitrary prime field double struck F sign p such that p > m. The proposed method is closely related to the minimal polynomial determination and therefore it has the following features: its complexity has little dependency on the size of characteristic p, its calculation cost is explicitly given with degree m, and it can generate primitive polynomials when pm - 1 is factorized as the product of prime numbers. The restriction p > m comes from using Newton's formula.

UR - http://www.scopus.com/inward/record.url?scp=58049083879&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049083879&partnerID=8YFLogxK

U2 - 10.1109/ICCIT.2008.171

DO - 10.1109/ICCIT.2008.171

M3 - Conference contribution

AN - SCOPUS:58049083879

SN - 9780769534077

T3 - Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008

SP - 478

EP - 485

BT - Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008

T2 - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008

Y2 - 11 November 2008 through 13 November 2008

ER -