A Twin for Euler’s φ Function in $\mathbb{F}_2[X]$
作者： R. Durán Díaz , J. Muñoz Masqué , A. Peinado Domínguez
DOI: 10.1007/978-3-540-73074-3_25
关键词: Euler's formula 、 Trinomial 、 Conjecture 、 Function (mathematics) 、 Primality test 、 Discrete mathematics 、 Mathematics Subject Classification 、 Mathematics 、 Factorization of polynomials 、 Simple (abstract algebra)
摘要: In this paper, we present a function in $\mathbb{F}_2[X]$ and prove that several of its properties closely resemble those Euler's i¾?function. Additionally, conjecture another property for can be used as simple primality test $\mathbb{F}_2[X]$, provide numerical evidence to support conjecture. Finally, further apply the previous results design trinomials. Mathematics Subject Classification 2000:Primary 13P05; Secondary 11T06, 12E05, 15A04.
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springerlink.com参考文章(13)
Jean-Jacques Quisquater, Mathieu Ciet, Francesco Sica, A Short Note on Irreducible Trinomials in Binary Fields ,(2002)
Daqing Wan, Alfred J Menezes, Ian F Blake, Xuhong Gao, Ronald C Mullin, Scott A Vanstone, Tomik Yaghoobian, Applications of Finite Fields ,(1992)
Ian F. Blake, Shuhong Gao, Robert Lambert, Constructive problems for irreducible polynomials over finite fields information theory and applications. pp. 1- 23 ,(1993) , 10.1007/3-540-57936-2_27
Rudolf Lidl, Harald Niederreiter, Introduction to finite fields and their applications The Mathematical Gazette. ,vol. 72, pp. 335- ,(1986) , 10.1017/CBO9781139172769
Joachim von zur Gathen, Irreducible trinomials over finite fields Mathematics of Computation. ,vol. 72, pp. 1987- 2000 ,(2003) , 10.1090/S0025-5718-03-01515-1
Neal Zierler, John Brillhart, On primitive trinomials (Mod 2) Information & Computation. ,vol. 13, pp. 541- 554 ,(1968) , 10.1016/S0019-9958(68)90973-X
Neal Zierler, On xn + x + 1 over GF(2) Information & Computation. ,vol. 16, pp. 502- 505 ,(1970) , 10.1016/S0019-9958(70)90264-0
H. Fredricksen, R. Wisniewski, On trinomials xn + x}2 + 1 and x8/ ± 3 + xk + 1 irreducible over GF(2) Information & Computation. ,vol. 50, pp. 58- 63 ,(1981) , 10.1016/S0019-9958(81)90144-3
Uzi Vishne, Factorization of Trinomials over Galois Fields of Characteristic 2 Finite Fields and Their Applications. ,vol. 3, pp. 370- 377 ,(1997) , 10.1006/FFTA.1997.0191
Joachim von zur Gathen, Daniel Panario, Factoring polynomials over finite fields: a survey Journal of Symbolic Computation. ,vol. 31, pp. 3- 17 ,(2001) , 10.1006/JSCO.1999.1002