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  • 1 Universität Bielefeld Fakultät für Mathematik Postfach 100131 D-33501 Bielefeld Germany E-mail Postfach 100131 D-33501 Bielefeld Germany E-mail
  • 2 Institut de Mathématiques de Luminy CNRS–UPR 9016 163 Avenue de Luminy, Case 907 F-13288 Marseille Cedex 9 France CNRS–UPR 9016 163 Avenue de Luminy, Case 907 F-13288 Marseille Cedex 9 France
  • 3 Eötvös Loránd University Department of Algebra and Number Theory H-1117 Budapest Pázmány Péter sétány 1/c Hungary E-mail H-1117 Budapest Pázmány Péter sétány 1/c Hungary E-mail
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Abstract  

In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography) it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated.

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