On the existence of pairs of primitive normal elements over finite fields

[1]  Xiwang Cao,et al.  On the existence of some specific elements in finite fields of characteristic 2 , 2012, Finite Fields Their Appl..

[2]  H. Davenport.  Bases for Finite Fields , 1968 .

[3]  Ronald C. Mullin,et al.  Optimal normal bases in GF(pn) , 1989, Discret. Appl. Math..

[4]  Giorgos Kapetanakis,et al.  An extension of the (strong) primitive normal basis theorem , 2014, Applicable Algebra in Engineering, Communication and Computing.

[5]  R. Sharma,et al.  Existence of pair of primitive elements over finite fields of characteristic 2 , 2018, Journal of Number Theory.

[6]  Stephen D. Cohen,et al.  Consecutive Primitive Roots in a Finite Field , 2010 .

[7]  L. Carlitz.  Some Problems Involving Primitive Roots in a Finite Field. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Jean-Guillaume Dumas,et al.  Efficient polynomial time algorithms computing industrial-strength primitive roots , 2004, Inf. Process. Lett..

[9]  Stephen D. Cohen.  Consecutive primitive roots in a finite field. II , 1985 .

[10]  The strong primitive normal basis theorem , 2006, math/0610400.

[11]  H. Lenstra,et al.  Primitive normal bases for finite fields , 1987 .

[13]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[14]  L Carlitz.  Some Problems Involving Primitive Roots in a Finite Field. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Stephen D. Cohen.  Pairs of primitive elements in fields of even order , 2014, Finite Fields Their Appl..

[16]  Giorgos Kapetanakis,et al.  Normal bases and primitive elements over finite fields , 2014, Finite Fields Their Appl..

[17]  L. Carlitz,et al.  Primitive roots in a finite field , 1952 .

[18]  D. Basnet,et al.  Sufficient condition for existence of special type of primitive normal elements over finite fields , 2019, 1902.04736.

[19]  R. K. Sharma,et al.  Existence of some special primitive normal elements over finite fields , 2017, Finite Fields Their Appl..

[20]  Stephen D. Cohen,et al.  Primitive values of quadratic polynomials in a finite field , 2018, Math. Comput..

[22]  F. N. Castro,et al.  Mixed exponential sums over finite fields , 2000 .

[23]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[24]  Tian Wen.  Primitive Normal Element and Its Inverse in Finite Fields , 2006 .

[25]  Gordon B. Agnew,et al.  An implementation for a fast public-key cryptosystem , 2004, Journal of Cryptology.

[26]  Cícero Carvalho,et al.  On special pairs of primitive elements over a finite field , 2021, Finite Fields Their Appl..

[27]  C. Carvalho,et al.  On existence of some special pair of primitive elements over finite fields , 2020, 2002.01867.