Sparse polynomials, redundant bases, gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields

Soonhak Kwon; Chang Hoon Kim; Chun Pyo Hong

doi:10.1007/s10623-006-9016-7

Sparse polynomials, redundant bases, gauss periods, and efficient exponentiation of primitive elements for small characteristic finite fields

Designs Codes and Cryptography ◽

10.1007/s10623-006-9016-7 ◽

2006 ◽

Vol 41 (3) ◽

pp. 299-306

Author(s):

Soonhak Kwon ◽

Chang Hoon Kim ◽

Chun Pyo Hong

Keyword(s):

Finite Fields ◽

Primitive Elements ◽

Sparse Polynomials ◽

Gauss Periods

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On primitive elements of finite fields avoiding affine hyperplanes

Finite Fields and Their Applications ◽

10.1016/j.ffa.2021.101911 ◽

2021 ◽

Vol 76 ◽

pp. 101911

Author(s):

Arthur Fernandes ◽

Lucas Reis

Keyword(s):

Finite Fields ◽

Primitive Elements

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

Journal of Number Theory ◽

10.1016/j.jnt.2018.05.016 ◽

2018 ◽

Vol 193 ◽

pp. 386-394 ◽

Cited By ~ 1

Author(s):

Rajendra K. Sharma ◽

Ambrish Awasthi ◽

Anju Gupta

Keyword(s):

Finite Fields ◽

Primitive Elements ◽

Characteristic 2

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Orders of Gauss Periods in Finite Fields

Applicable Algebra in Engineering Communication and Computing ◽

10.1007/s002000050093 ◽

1998 ◽

Vol 9 (1) ◽

pp. 15-24 ◽

Cited By ~ 18

Author(s):

Joachim von zur Gathen ◽

Igor Shparlinski

Keyword(s):

Finite Fields ◽

Gauss Periods

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Some primitive elements for the Artin–Schreier extensions of finite fields

Journal of Mathematical Sciences ◽

10.1007/s10958-015-2548-5 ◽

2015 ◽

Vol 210 (1) ◽

pp. 67-75 ◽

Cited By ~ 1

Author(s):

Roman B. Popovych

Keyword(s):

Finite Fields ◽

Primitive Elements

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Exponential Sums with Sparse Polynomials over Finite Fields

SIAM Journal on Discrete Mathematics ◽

10.1137/20m1357731 ◽

2021 ◽

Vol 35 (2) ◽

pp. 976-987

Author(s):

Igor E. Shparlinski ◽

Qiang Wang

Keyword(s):

Finite Fields ◽

Exponential Sums ◽

Sparse Polynomials ◽

Polynomials Over Finite Fields

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Pair of primitive elements with prescribed traces over finite fields

Communications in Algebra ◽

10.1080/00927872.2018.1503283 ◽

2019 ◽

Vol 47 (3) ◽

pp. 1278-1286 ◽

Cited By ~ 2

Author(s):

R. K. Sharma ◽

Anju Gupta

Keyword(s):

Finite Fields ◽

Primitive Elements

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Gauss periods and fast exponentiation in finite fields

LATIN '95: Theoretical Informatics - Lecture Notes in Computer Science ◽

10.1007/3-540-59175-3_98 ◽

1995 ◽

pp. 311-322 ◽

Cited By ~ 23

Author(s):

Shuhong Gao ◽

Joachim von zur Gathen ◽

Daniel Panario

Keyword(s):

Finite Fields ◽

Gauss Periods

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Primitive elements in finite fields and costas arrays

Applicable Algebra in Engineering Communication and Computing ◽

10.1007/bf01810854 ◽

1991 ◽

Vol 2 (1) ◽

pp. 45-53 ◽

Cited By ~ 11

Author(s):

Stephen D. Cohen ◽

Gary L. Mullen

Keyword(s):

Finite Fields ◽

Primitive Elements

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Normal bases and primitive elements over finite fields

Finite Fields and Their Applications ◽

10.1016/j.ffa.2013.12.002 ◽

2014 ◽

Vol 26 ◽

pp. 123-143 ◽

Cited By ~ 6

Author(s):

Giorgos Kapetanakis

Keyword(s):

Finite Fields ◽

Primitive Elements ◽

Normal Bases

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Noisy interpolation of sparse polynomials in finite fields

Applicable Algebra in Engineering Communication and Computing ◽

10.1007/s00200-005-0180-1 ◽

2005 ◽

Vol 16 (5) ◽

pp. 307-317 ◽

Cited By ~ 6

Author(s):

Igor Shparlinski ◽

Arne Winterhof

Keyword(s):

Finite Fields ◽

Sparse Polynomials

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