\contentsline {section}{\numberline {I}Introduction}{2}
\contentsline {section}{\numberline {II}Mathematical background}{2}
\contentsline {subsection}{\numberline {II-A}Finite Fields}{2}
\contentsline {subsection}{\numberline {II-B}Discrete Fourier Transform (DFT)}{2}
\contentsline {subsection}{\numberline {II-C}Multi-dimensional DFTs}{4}
\contentsline {section}{\numberline {III}S-hash Arithmetic}{5}
\contentsline {subsection}{\numberline {III-A}The field $GF(17)$}{5}
\contentsline {subsection}{\numberline {III-B}The Fast Fourier Transform}{6}
\contentsline {subsection}{\numberline {III-C}The field $GF(2^4)$}{6}
\contentsline {subsubsection}{\numberline {III-C.1}Addition}{6}
\contentsline {subsubsection}{\numberline {III-C.2}Multiplication}{6}
\contentsline {subsubsection}{\numberline {III-C.3}Inversion}{6}
\contentsline {subsubsection}{\numberline {III-C.4}Affine transformation}{6}
\contentsline {subsection}{\numberline {III-D}SRC (shift row \& column)}{7}
\contentsline {subsection}{\numberline {III-E}Component-wise operations}{7}
\contentsline {section}{\numberline {IV}Specral Hashing Algorithm}{8}
\contentsline {subsection}{\numberline {IV-A}Initialization}{8}
\contentsline {subsection}{\numberline {IV-B}Compression function}{9}
\contentsline {subsection}{\numberline {IV-C}Hash generation}{15}
\contentsline {section}{\numberline {V}Security Considerations}{16}
\contentsline {section}{\numberline {VI}Conclusions}{16}
\contentsline {section}{References}{17}