{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.1}The generation of pseudorandom sequence}{\reset@font\mtcSfont 20}{section.9.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.1.1}The logistic map}{\reset@font\mtcSSfont 20}{subsection.9.1.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.1.2}XORshift}{\reset@font\mtcSSfont 20}{subsection.9.1.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.1.3}ISAAC}{\reset@font\mtcSSfont 20}{subsection.9.1.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.2}A Theoretical Proof for Devaney's Chaotic Dynamical Systems}{\reset@font\mtcSfont 21}{section.9.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.1}A topological approach for chaotic iterations}{\reset@font\mtcSSfont 22}{subsection.9.2.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.2}Regularity}{\reset@font\mtcSSfont 22}{subsection.9.2.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.3}Transitivity}{\reset@font\mtcSSfont 23}{subsection.9.2.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.4}Sensitive dependence on initial conditions}{\reset@font\mtcSSfont 23}{subsection.9.2.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.2.5}Devaney's Chaotic Dynamical Systems}{\reset@font\mtcSSfont 23}{subsection.9.2.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.3}Old CI algorithms and examples}{\reset@font\mtcSfont 24}{section.9.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.3.1}Chaotic iterations as PRNG}{\reset@font\mtcSSfont 24}{subsection.9.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.3.2} The range of $m^i$: $\mathcal {M}$}{\reset@font\mtcSSfont 24}{subsection.9.3.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.3.3}Old CI PRNGs Algorithm}{\reset@font\mtcSSfont 27}{subsection.9.3.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.3.4}Illustrative example}{\reset@font\mtcSSfont 27}{subsection.9.3.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.3.5}On the periodicity of chaotic orbit}{\reset@font\mtcSSfont 27}{subsection.9.3.5}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {3.4}New CI algorithms and examples}{\reset@font\mtcSfont 29}{section.9.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.4.1}Presentation}{\reset@font\mtcSSfont 29}{subsection.9.4.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.4.2}The seed}{\reset@font\mtcSSfont 30}{subsection.9.4.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.4.3}Sequence $m$ of returned states}{\reset@font\mtcSSfont 30}{subsection.9.4.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.4.4}Chaotic strategy}{\reset@font\mtcSSfont 31}{subsection.9.4.4}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.4.5}New CI(XORshift, XORshift) Algorithm}{\reset@font\mtcSSfont 31}{subsection.9.4.5}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {3.4.6}Illustrative Example}{\reset@font\mtcSSfont 33}{subsection.9.4.6}}