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New pseudorandom sequences constructed by quadratic residues and Lehmer numbers

Authors:	Huaning Liu

Institution:	Department of Mathematics, Northwest University, Xi'an, Shaanxi, People's Republic of China

Abstract:	Let be an odd prime. Define $\displaystyle e_n=\left\{\begin{array}{ll}\displaystyle (-1)^{n+\overline{n}}, ... ...e{n}+1}, & \hbox{if $n$ is a quadratic nonresidue mod $p$}, \end{array}\right.$ where $\overline{n}$ is the multiplicative inverse of modulo such that $1\leq \overline{n}\leq p-1$ . This paper shows that the sequence $\{e_n\}$ is a ``good" pseudorandom sequence, by using the properties of exponential sums, character sums, Kloosterman sums and mean value theorems of Dirichlet -functions.

Keywords:	Pseudorandom binary sequence inverse

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