scholarly journals On equations of finite fields of characteristic 2 and APN functions

2015 ◽  
Vol 12 (2-3) ◽  
pp. 75-93
Author(s):  
Nobuo Nakagawa
Keyword(s):  
Finite Fields ◽  
Apn Functions ◽  
Characteristic 2

scholarly journals On the existence of some specific elements in finite fields of characteristic 2

2012 ◽  
Vol 18 (4) ◽  
pp. 800-813 ◽  
Author(s):  
Peipei Wang ◽  
Xiwang Cao ◽  
Rongquan Feng
Keyword(s):  
Finite Fields ◽  
Characteristic 2

scholarly journals Monomial Generalized Almost Perfect Nonlinear Functions

2020 ◽  
Vol 31 (03) ◽  
pp. 411-419
Author(s):  
Masamichi Kuroda
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Algebraic Degree ◽  
Apn Functions ◽  
Nonlinear Functions ◽  
Almost Perfect Nonlinear ◽  
Basic Properties ◽  
Almost Perfect Nonlinear Functions

Generalized almost perfect nonlinear (GAPN) functions were defined to satisfy some generalizations of basic properties of almost perfect nonlinear (APN) functions for even characteristic. In particular, on finite fields of even characteristic, GAPN functions coincide with APN functions. In this paper, we study monomial GAPN functions for odd characteristic. We give monomial GAPN functions whose algebraic degree are maximum or minimum on a finite field of odd characteristic. Moreover, we define a generalization of exceptional APN functions and give typical examples.

Existence of pair of primitive elements over finite fields of characteristic 2

2018 ◽  
Vol 193 ◽  
pp. 386-394 ◽  
Author(s):  
Rajendra K. Sharma ◽  
Ambrish Awasthi ◽  
Anju Gupta
Keyword(s):  
Finite Fields ◽  
Primitive Elements ◽  
Characteristic 2
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