1,336 research outputs found
Error linear complexity measures for multisequences
Complexity measures for sequences over finite fields, such as the linear complexity and the k-error linear complexity, play an important role in cryptology. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multisequences. We introduce various options for error linear complexity measures for multisequences. For finite multisequences as well as for periodic multisequences with prime period, we present formulas for the number of multisequences with given error linear complexity for several cases, and we present lower bounds for the expected error linear complexity
Discrepancy-based error estimates for Quasi-Monte Carlo. I: General formalism
We show how information on the uniformity properties of a point set employed
in numerical multidimensional integration can be used to improve the error
estimate over the usual Monte Carlo one. We introduce a new measure of
(non-)uniformity for point sets, and derive explicit expressions for the
various entities that enter in such an improved error estimate. The use of
Feynman diagrams provides a transparent and straightforward way to compute this
improved error estimate.Comment: 23 pages, uses axodraw.sty, available at
ftp://nikhefh.nikhef.nl/pub/form/axodraw Fixed some typos, tidied up section
3.
Multisequences with high joint nonlinear complexity
We introduce the new concept of joint nonlinear complexity for multisequences
over finite fields and we analyze the joint nonlinear complexity of two
families of explicit inversive multisequences. We also establish a
probabilistic result on the behavior of the joint nonlinear complexity of
random multisequences over a fixed finite field
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