scholarly journals The determinant of random power series matrices over finite fields

2000 ◽  
Vol 315 (1-3) ◽  
pp. 139-144 ◽  
Author(s):  
Khaled A.S. Abdel-Ghaffar
Keyword(s):  
Power Series ◽  
Finite Fields ◽  
Random Power Series

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 On Inhomogeneous Bernoulli Convolutions and Random Power Series

2011 ◽  
Vol 36 (1) ◽  
pp. 213 ◽  
Author(s):  
Antonios Bisbas ◽  
Jörg Neunhäuserer
Keyword(s):  
Power Series ◽  
Random Power Series ◽  
Bernoulli Convolutions

scholarly journals Divergence of random power series.

1959 ◽  
Vol 6 (4) ◽  
pp. 343-347 ◽  
Author(s):  
A. Dvoretzky ◽  
P. Erdős
Keyword(s):  
Power Series ◽  
Random Power Series

scholarly journals A theorem on power series with applications to classical groups over finite fields

2001 ◽  
Vol 64 (1) ◽  
pp. 121-129
Author(s):  
Andrew J. Spencer
Keyword(s):  
Power Series ◽  
Finite Fields ◽  
Generating Functions ◽  
General Linear ◽  
Classical Groups ◽  
Orthogonal Groups

For some of the classical groups over finite fields it is possible to express the proportion of eigenvalue-free matrices in terms of generating functions. We prove a theorem on the monotonicity of the coefficients of powers of power series and apply this to the generating functions of the general linear, symplectic and orthogonal groups. This proves a conjecture on the monotonicity of the proportions of eigenvalue-free elements in these groups.

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