A conjecture on permutation trinomials over finite fields of characteristic two

Nian Li;  ; Qiaoyu Hu;

doi:10.3934/amc.2019031

A conjecture on permutation trinomials over finite fields of characteristic two

Advances in Mathematics of Communications ◽

10.3934/amc.2019031 ◽

2019 ◽

Vol 13 (3) ◽

pp. 505-512

Author(s):

Nian Li ◽

◽

Qiaoyu Hu ◽

Keyword(s):

Finite Fields ◽

Characteristic Two ◽

Permutation Trinomials

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Graphs associated with the map 𝑥\𝑚𝑎𝑝𝑠𝑡𝑜𝑥+𝑥⁻¹ in finite fields of characteristic two

Theory and Applications of Finite Fields - Contemporary Mathematics ◽

10.1090/conm/579/11530 ◽

2012 ◽

pp. 187-204 ◽

Cited By ~ 4

Author(s):

S. Ugolini

Keyword(s):

Finite Fields ◽

Characteristic Two

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Fast transforms over finite fields of characteristic two

Journal of Symbolic Computation ◽

10.1016/j.jsc.2020.10.002 ◽

2021 ◽

Vol 104 ◽

pp. 824-854

Author(s):

Nicholas Coxon

Keyword(s):

Finite Fields ◽

Fast Transforms ◽

Characteristic Two

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Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree

Lecture Notes in Computer Science - Progress in Cryptology — INDOCRYPT 2001 ◽

10.1007/3-540-45311-3_19 ◽

2001 ◽

pp. 195-213 ◽

Cited By ~ 9

Author(s):

Markus Maurer ◽

Alfred Menezes ◽

Edlyn Teske

Keyword(s):

Finite Fields ◽

Characteristic Two ◽

Weil Descent

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Permutation polynomials of the form cx + Tr q l / q ( x a ) $cx+\text {Tr}_{q^{l}/ q}(x^{a})$ and permutation trinomials over finite fields with even characteristic

Cryptography and Communications ◽

10.1007/s12095-017-0236-7 ◽

2017 ◽

Vol 10 (3) ◽

pp. 531-554 ◽

Cited By ~ 12

Author(s):

Kangquan Li ◽

Longjiang Qu ◽

Xi Chen ◽

Chao Li

Keyword(s):

Finite Fields ◽

Permutation Polynomials ◽

Permutation Trinomials

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Triple-Cycle Permutations Over Finite Fields of Characteristic Two

International Journal of Foundations of Computer Science ◽

10.1142/s0129054119500059 ◽

2019 ◽

Vol 30 (02) ◽

pp. 275-292

Author(s):

Xianping Liu ◽

Yuan Chen ◽

Yunge Xu ◽

Zhimin Sun

Keyword(s):

Finite Fields ◽

Characteristic Two

Triple-cycle permutations over finite fields of characteristic two are studied, and some classes of triple-cycle permutations are proposed in this paper. In addition, new triple-cycle permutations can be constructed by switching construction from known ones.

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Computing Logarithms in Finite Fields of Characteristic Two

SIAM Journal on Algebraic and Discrete Methods ◽

10.1137/0605029 ◽

1984 ◽

Vol 5 (2) ◽

pp. 276-285 ◽

Cited By ~ 44

Author(s):

I. F. Blake ◽

R. Fuji-Hara ◽

R. C. Mullin ◽

S. A. Vanstone

Keyword(s):

Finite Fields ◽

Characteristic Two

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Non-hyperelliptic curves of genus three over finite fields of characteristic two

Journal of Number Theory ◽

10.1016/j.jnt.2005.05.014 ◽

2006 ◽

Vol 116 (2) ◽

pp. 443-473 ◽

Cited By ~ 4

Author(s):

Enric Nart ◽

Christophe Ritzenthaler

Keyword(s):

Finite Fields ◽

Hyperelliptic Curves ◽

Characteristic Two ◽

Curves Of Genus Three

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Some new classes of permutation trinomials over finite fields with even characteristic

Finite Fields and Their Applications ◽

10.1016/j.ffa.2016.05.004 ◽

2016 ◽

Vol 41 ◽

pp. 89-96 ◽

Cited By ~ 38

Author(s):

Rohit Gupta ◽

R.K. Sharma

Keyword(s):

Finite Fields ◽

Permutation Trinomials

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Low Complexity Normal Elements over Finite Fields of Characteristic Two

IEEE Transactions on Computers ◽

10.1109/tc.2007.70845 ◽

2008 ◽

Vol 57 (7) ◽

pp. 990-1001 ◽

Cited By ~ 4

Author(s):

Ariane M. Masuda ◽

Lucia Moura ◽

Daniel Panario ◽

David Thomson

Keyword(s):

Finite Fields ◽

Low Complexity ◽

Characteristic Two

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Primitive Polynomials over Finite Fields of Characteristic Two

Applicable Algebra in Engineering Communication and Computing ◽

10.1007/s00200-003-0140-6 ◽

2004 ◽

Vol 14 (5) ◽

pp. 381-395 ◽

Cited By ~ 14

Author(s):

Fan Shuqin ◽

Han Wenbao

Keyword(s):

Finite Fields ◽

Primitive Polynomials ◽

Polynomials Over Finite Fields ◽

Characteristic Two

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