{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.1}The Legendre PRF and Context}{\reset@font\mtcSfont 60}{section.4.1}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode The Legendre PRF.}{\reset@font\mtcPfont 60}{section*.57}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Previous Results.}{\reset@font\mtcPfont 61}{section*.58}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode On the Use of QRACM.}{\reset@font\mtcPfont 61}{section*.59}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.2}Table-based Attacks}{\reset@font\mtcSfont 62}{section.4.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.2.1}Classical Algorithm}{\reset@font\mtcSSfont 62}{subsection.4.2.1}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Quantum Version with QRACM.}{\reset@font\mtcPfont 63}{section*.60}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.2.2}Quantum Search with Early Abort}{\reset@font\mtcSSfont 63}{subsection.4.2.2}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Early-aborting.}{\reset@font\mtcPfont 64}{section*.61}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.2.3}Distinguished Collisions}{\reset@font\mtcSSfont 64}{subsection.4.2.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.3}A Reversible Version of Kuperberg's Algorithm}{\reset@font\mtcSfont 66}{section.4.3}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.1}The Decisional Hidden Shift Problem}{\reset@font\mtcSSfont 66}{subsection.4.3.1}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.2}Kuperberg's Algorithm Made Reversible}{\reset@font\mtcSSfont 66}{subsection.4.3.2}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Sample Database.}{\reset@font\mtcPfont 66}{section*.62}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.3}Label States and Label Qubits}{\reset@font\mtcSSfont 67}{subsection.4.3.3}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Classical Combinations.}{\reset@font\mtcPfont 68}{section*.63}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Complexity.}{\reset@font\mtcPfont 68}{section*.64}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.4}Combining Two Labels Reversibly}{\reset@font\mtcSSfont 68}{subsection.4.3.4}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Choosing which Labels to Combine.}{\reset@font\mtcPfont 69}{section*.66}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.5}Combining All Labels}{\reset@font\mtcSSfont 69}{subsection.4.3.5}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Sorting Network.}{\reset@font\mtcPfont 70}{section*.67}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode The Full Circuit.}{\reset@font\mtcPfont 70}{section*.68}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.6}Behavior in the Non-shifted Case}{\reset@font\mtcSSfont 71}{subsection.4.3.6}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.3.7}Bounding the Errors}{\reset@font\mtcSSfont 71}{subsection.4.3.7}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode False Negatives.}{\reset@font\mtcPfont 71}{section*.69}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode False Positives.}{\reset@font\mtcPfont 72}{section*.70}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.4}Quantum Search with an Approximate Test}{\reset@font\mtcSfont 72}{section.4.4}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.5}The Offline-DAHS Algorithm}{\reset@font\mtcSfont 75}{section.4.5}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.5.1}High-level Description}{\reset@font\mtcSSfont 75}{subsection.4.5.1}}
{\reset@font\mtcPfont\mtc@string\contentsline{paragraph}{\noexpand \leavevmode Description.}{\reset@font\mtcPfont 75}{section*.71}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.5.2}Approximate Promise}{\reset@font\mtcSSfont 76}{subsection.4.5.2}}
{\reset@font\mtcSSfont\mtc@string\contentsline{subsection}{\noexpand \leavevmode \numberline {4.5.3}Application to the Legendre Symbol}{\reset@font\mtcSSfont 77}{subsection.4.5.3}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.6}Detailed Complexities}{\reset@font\mtcSfont 78}{section.4.6}}
{\reset@font\mtcSfont\mtc@string\contentsline{section}{\noexpand \leavevmode \numberline {4.7}Conclusion}{\reset@font\mtcSfont 78}{section.4.7}}
