Design sequences with high linear complexity over finite fields using generalized cyclotomy

2016 ◽  
Vol 9 (6) ◽  
pp. 683-691 ◽  
Author(s):  
Vladimir Edemskiy ◽  
Xiaoni Du
Keyword(s):  
Finite Fields ◽  
Linear Complexity ◽  
Generalized Cyclotomy

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

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.

Cyclotomy and arithmetic properties of some families in Z[x]/〈xpq − 1〉

2019 ◽  
Vol 13 (04) ◽  
pp. 2050077
Author(s):  
Sonal Jain ◽  
Sudhir Batra
Keyword(s):  
Finite Fields ◽  
Alternate Proof ◽  
Generalized Cyclotomy ◽  
Cyclotomic Cosets ◽  
Arithmetic Properties

Cyclotomic classes of order 2 with respect to a product of two distinct odd primes [Formula: see text] and [Formula: see text] are represented in some specific forms and using these forms an alternate proof of Theorem 3 of [C. Ding and T. Helleseth, New generalized cyclotomy and its applications, Finite Fields Appl. 4 (1998) 140–166] is given, when [Formula: see text]. Further, it is observed that these classes are related to [Formula: see text]-cyclotomic cosets, where [Formula: see text] and [Formula: see text] such that gcd([Formula: see text]. Finally, arithmetic properties of some families in [Formula: see text] and hence in [Formula: see text] are studied.

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 Constructions of Sequences with Almost Perfect Linear Complexity Profile from Curves over Finite Fields

1999 ◽  
Vol 5 (3) ◽  
pp. 301-313 ◽  
Author(s):  
Chaoping Xing ◽  
Harald Niederreiter ◽  
Kwok Yan Lam ◽  
Cunsheng Ding
Keyword(s):  
Finite Fields ◽  
Linear Complexity ◽  
Curves Over Finite Fields ◽  
Linear Complexity Profile
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