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Construction des suites binaires pseudo-aléatoires

Abstract : This thesis presents some constructions of pseudo-random sequences inspired by natural questions in number theory. We use two measures introduced by A. Sarkozy et C. Mauduit to discuss some aspects of a priori testing of these sequences. They are the well-distribution measure and correlation measure of order k. On the one hand, thanks to a work of A. Weil, some Dirichlet characters give a large family of interesting examples of constructions. On the other hand, our study on a construction based on the distribution of the greatest prime factors do not supply any sufficiently exploitable estimate. However, we observe the bias on some congruence classes of prime factors. We also discuss some probability aspects of both measures. A brief history on the randomness is presented to help better comprehension, as well as some subjects in cryptology which are given in an appendix.
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Shea Ming Oon. Construction des suites binaires pseudo-aléatoires. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2005. Français. ⟨NNT : 2005NAN10017⟩. ⟨tel-01754341⟩



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