Propriétés aléatoires des suites d'entiers

Abstract : The generation of pseudorandom numbers plays an important role in many fields of mathematics and physics, in particular in the problems of cryptography. In 1997 C. Mauduit and A. Sarkozy introduced new measures of pseudorandomness of binary sequences: the well-distribution measure and the correlation measure. In the second chapter of the thesis we define a further new measure of pseudorandomness: the symmetry measure. In the third chapter of the thesis we constructed a large family of pseudorandom sequences by using the discrete logarithm. The sequences in this construction have strong pseudorandom properties, but they can be generated very slowly. In the fourth chapter we will improve on this construction by replacing a sequence which can be generated faster. In the last two chapters of the thesis we study inequalities between the measures of pseudorandomness. Among others, a conjecture of C. Mauduit is proved.
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Katalin Gyarmati. Propriétés aléatoires des suites d'entiers. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2005. Français. ⟨NNT : 2005NAN10001⟩. ⟨tel-01777289⟩

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