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

Hiroaki Nasu; Yasuyuki Nogami; Yoshitaka Morikawa; Shigeki Kobayashi; Tatsuo Sugimura

doi:10.1109/ICCIT.2008.171

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

Hiroaki Nasu, Yasuyuki Nogami, Yoshitaka Morikawa, Shigeki Kobayashi, Tatsuo Sugimura

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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 p^m - 1 is factorized as the product of prime numbers. The restriction p > m comes from using Newton's formula.

Original language	English
Title of host publication	Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008
Pages	478-485
Number of pages	8
DOIs	https://doi.org/10.1109/ICCIT.2008.171
Publication status	Published - Dec 31 2008
Event	3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008 - Busan, Korea, Republic of Duration: Nov 11 2008 → Nov 13 2008

Publication series

Name	Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008
Volume	2

Other

Other	3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008
Country/Territory	Korea, Republic of
City	Busan
Period	11/11/08 → 11/13/08

ASJC Scopus subject areas

Information Systems
Software

Access to Document

10.1109/ICCIT.2008.171

Cite this

Nasu, H., Nogami, Y., Morikawa, Y., Kobayashi, S., & Sugimura, T. (2008). Systematic generation of an irreducible polynomial of an arbitrary degree m over double struck F sign_p such That p > m. In Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008 (pp. 478-485). Article 4682287 (Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008; Vol. 2). https://doi.org/10.1109/ICCIT.2008.171

Systematic generation of an irreducible polynomial of an arbitrary degree m over double struck F sign_p such That p > m. / Nasu, Hiroaki; Nogami, Yasuyuki; Morikawa, Yoshitaka et al.
Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008. 2008. p. 478-485 4682287 (Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Nasu, H, Nogami, Y, Morikawa, Y, Kobayashi, S & Sugimura, T 2008, Systematic generation of an irreducible polynomial of an arbitrary degree m over double struck F sign_p such That p > m. in Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008., 4682287, Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008, vol. 2, pp. 478-485, 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008, Busan, Korea, Republic of, 11/11/08. https://doi.org/10.1109/ICCIT.2008.171

Nasu H, Nogami Y, Morikawa Y, Kobayashi S, Sugimura T. Systematic generation of an irreducible polynomial of an arbitrary degree m over double struck F sign_p such That p > m. In Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008. 2008. p. 478-485. 4682287. (Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008). doi: 10.1109/ICCIT.2008.171

Nasu, Hiroaki ; Nogami, Yasuyuki ; Morikawa, Yoshitaka et al. / Systematic generation of an irreducible polynomial of an arbitrary degree m over double struck F sign_p such That p > m. Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008. 2008. pp. 478-485 (Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008).

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