scholarly journals Multi-sequences with Almost Perfect Linear Complexity Profile and Function Fields over Finite Fields

2000 ◽  
Vol 16 (4) ◽  
pp. 661-675 ◽  
Author(s):  
Chaoping Xing
Keyword(s):  
Finite Fields ◽  
Linear Complexity ◽  
Function Fields ◽  
Linear Complexity Profile ◽  
And Function

scholarly journals On the use of expansion series for stream ciphers

2012 ◽  
Vol 15 ◽  
pp. 326-340 ◽  
Author(s):  
Claus Diem
Keyword(s):  
Power Series ◽  
Finite Fields ◽  
Linear Complexity ◽  
Stream Ciphers ◽  
Series Expansions ◽  
Expansion Series ◽  
Power Series Expansions ◽  
Curves Over Finite Fields ◽  
Linear Complexity Profile ◽  
Natural Way

AbstractFrom power series expansions of functions on curves over finite fields, one can obtain sequences with perfect or almost perfect linear complexity profile. It has been suggested by various authors to use such sequences as key streams for stream ciphers. In this work, we show how long parts of such sequences can be computed efficiently from short ones. Such sequences should therefore be considered to be cryptographically weak. Our attack leads in a natural way to a new measure of the complexity of sequences which we call expansion complexity.

scholarly journals Expansion complexity and linear complexity of sequences over finite fields

2016 ◽  
Vol 9 (4) ◽  
pp. 501-509 ◽  
Author(s):  
László Mérai ◽  
Harald Niederreiter ◽  
Arne Winterhof
Keyword(s):  
Finite Fields ◽  
Linear Complexity

scholarly journals Pinchuk maps and function fields

2014 ◽  
Vol 218 (2) ◽  
pp. 297-302
Author(s):  
L. Andrew Campbell
Keyword(s):  
Function Fields ◽  
And Function

scholarly journals Extremal behaviour of ± 1-valued completely multiplicative functions in function fields

2021 ◽  
Vol 56 (1) ◽  
pp. 79-94
Author(s):  
Nikola Lelas ◽  
Keyword(s):  
Rational Function ◽  
Finite Fields ◽  
Function Fields ◽  
Mean Value ◽  
Multiplicative Functions ◽  
Irreducible Polynomials ◽  
Liouville Function ◽  
The Mean

We investigate the classical Pólya and Turán conjectures in the context of rational function fields over finite fields 𝔽q. Related to these two conjectures we investigate the sign of truncations of Dirichlet L-functions at point s=1 corresponding to quadratic characters over 𝔽q[t], prove a variant of a theorem of Landau for arbitrary sets of monic, irreducible polynomials over 𝔽q[t] and calculate the mean value of certain variants of the Liouville function over 𝔽q[t].

A new class of quaternary generalized cyclotomic sequences of order 2d and length 2pm with high linear complexity

2018 ◽  
Vol 16 (01) ◽  
pp. 1850006 ◽  
Author(s):  
Longfei Liu ◽  
Xiaoyuan Yang ◽  
Bin Wei ◽  
Liqiang Wu
Keyword(s):  
Finite Fields ◽  
Linear Complexity ◽  
Periodic Sequences ◽  
New Class ◽  
New Family ◽  
Generalized Cyclotomic Classes ◽  
Cyclotomic Sequences

Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudo-random properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. In this paper, we construct a new family of quaternary generalized cyclotomic sequences with order [Formula: see text] and length [Formula: see text], which generalize the sequences constructed by Ke et al. in 2012. In addition, we determine its linear complexity using cyclotomic theory. The conclusions reveal that these sequences have high linear complexity, which means they can resist linear attacks.

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