\hypertarget{elgamal_8h}{
\section{include/beecrypt/elgamal.h File Reference}
\label{elgamal_8h}\index{include/beecrypt/elgamal.h@{include/beecrypt/elgamal.h}}
}
ElGamal algorithm.
{\ttfamily \#include \char`\"{}beecrypt/mpbarrett.h\char`\"{}}\par
Include dependency graph for elgamal.h:
\nopagebreak
\begin{figure}[H]
\begin{center}
\leavevmode
\includegraphics[width=212pt]{elgamal_8h__incl}
\end{center}
\end{figure}
\subsection*{Functions}
\begin{DoxyCompactItemize}
\item
int \hyperlink{elgamal_8h_a71210da412fefa0f230a7f988eb83c31}{elgv1sign} (const \hyperlink{structmpbarrett}{mpbarrett} $\ast$p, const \hyperlink{structmpbarrett}{mpbarrett} $\ast$n, const \hyperlink{structmpnumber}{mpnumber} $\ast$g, \hyperlink{structrandomGeneratorContext}{randomGeneratorContext} $\ast$, const \hyperlink{structmpnumber}{mpnumber} $\ast$hm, const \hyperlink{structmpnumber}{mpnumber} $\ast$x, \hyperlink{structmpnumber}{mpnumber} $\ast$r, \hyperlink{structmpnumber}{mpnumber} $\ast$s)
\begin{DoxyCompactList}\small\item\em This function performs raw ElGamal signing, variant 1. \item\end{DoxyCompactList}\item
int \hyperlink{elgamal_8h_ab5a4857d59add82a522e0c08c83298f8}{elgv3sign} (const \hyperlink{structmpbarrett}{mpbarrett} $\ast$p, const \hyperlink{structmpbarrett}{mpbarrett} $\ast$n, const \hyperlink{structmpnumber}{mpnumber} $\ast$g, \hyperlink{structrandomGeneratorContext}{randomGeneratorContext} $\ast$, const \hyperlink{structmpnumber}{mpnumber} $\ast$hm, const \hyperlink{structmpnumber}{mpnumber} $\ast$x, \hyperlink{structmpnumber}{mpnumber} $\ast$r, \hyperlink{structmpnumber}{mpnumber} $\ast$s)
\begin{DoxyCompactList}\small\item\em This function performs raw ElGamal signing, variant 3. \item\end{DoxyCompactList}\item
int \hyperlink{elgamal_8h_ab91d86edb1453350a8e4023e694474ec}{elgv1vrfy} (const \hyperlink{structmpbarrett}{mpbarrett} $\ast$p, const \hyperlink{structmpbarrett}{mpbarrett} $\ast$n, const \hyperlink{structmpnumber}{mpnumber} $\ast$g, const \hyperlink{structmpnumber}{mpnumber} $\ast$hm, const \hyperlink{structmpnumber}{mpnumber} $\ast$y, const \hyperlink{structmpnumber}{mpnumber} $\ast$r, const \hyperlink{structmpnumber}{mpnumber} $\ast$s)
\begin{DoxyCompactList}\small\item\em This function performs raw ElGamal verification, variant 1. \item\end{DoxyCompactList}\item
int \hyperlink{elgamal_8h_aaa1c3bb1ca269e9b40ee8a561a3f78f6}{elgv3vrfy} (const \hyperlink{structmpbarrett}{mpbarrett} $\ast$p, const \hyperlink{structmpbarrett}{mpbarrett} $\ast$n, const \hyperlink{structmpnumber}{mpnumber} $\ast$g, const \hyperlink{structmpnumber}{mpnumber} $\ast$hm, const \hyperlink{structmpnumber}{mpnumber} $\ast$y, const \hyperlink{structmpnumber}{mpnumber} $\ast$r, const \hyperlink{structmpnumber}{mpnumber} $\ast$s)
\begin{DoxyCompactList}\small\item\em This function performs raw ElGamal verification, variant 3. \item\end{DoxyCompactList}\end{DoxyCompactItemize}
\subsection{Detailed Description}
ElGamal algorithm. For more information on this algorithm, see: \char`\"{}Handbook of Applied Cryptography\char`\"{}, 11.5.2: \char`\"{}The ElGamal signature scheme\char`\"{}, p. 454-\/459
Two of the signature variants in Note 11.70 are implemented.
\begin{Desc}
\item[\hyperlink{todo__todo000002}{Todo}]Implement ElGamal encryption and decryption.\end{Desc}
\begin{Desc}
\item[\hyperlink{todo__todo000003}{Todo}]Explore the possibility of using simultaneous multiple exponentiation, as described in HAC, 14.87 (iii).\end{Desc}
\begin{DoxyAuthor}{Author}
Bob Deblier $<$\href{mailto:bob.deblier@telenet.be}{\tt bob.deblier@telenet.be}$>$
\end{DoxyAuthor}
\subsection{Function Documentation}
\hypertarget{elgamal_8h_a71210da412fefa0f230a7f988eb83c31}{
\index{elgamal.h@{elgamal.h}!elgv1sign@{elgv1sign}}
\index{elgv1sign@{elgv1sign}!elgamal.h@{elgamal.h}}
\subsubsection[{elgv1sign}]{\setlength{\rightskip}{0pt plus 5cm}int elgv1sign (
\begin{DoxyParamCaption}
\item[{const {\bf mpbarrett} $\ast$}]{p, }
\item[{const {\bf mpbarrett} $\ast$}]{n, }
\item[{const {\bf mpnumber} $\ast$}]{g, }
\item[{{\bf randomGeneratorContext} $\ast$}]{rgc, }
\item[{const {\bf mpnumber} $\ast$}]{hm, }
\item[{const {\bf mpnumber} $\ast$}]{x, }
\item[{{\bf mpnumber} $\ast$}]{r, }
\item[{{\bf mpnumber} $\ast$}]{s}
\end{DoxyParamCaption}
)}}
\label{elgamal_8h_a71210da412fefa0f230a7f988eb83c31}
This function performs raw ElGamal signing, variant 1.
Signing equations:
\begin{DoxyItemize}
\item $r=g^{k}\ \textrm{mod}\ p$ \item $s=k^{-1}(h(m)-xr)\ \textrm{mod}\ (p-1)$\end{DoxyItemize}
\begin{DoxyParams}{Parameters}
{\em p} & The prime. \\
\hline
{\em n} & The reducer mod (p-\/1). \\
\hline
{\em g} & The generator. \\
\hline
{\em rgc} & The pseudo-\/random generat \\
\hline
{\em hm} & The hash to be signed. \\
\hline
{\em x} & The private key value. \\
\hline
{\em r} & The signature's {\itshape r\/} value. \\
\hline
{\em s} & The signature's {\itshape s\/} value. \\
\hline
\end{DoxyParams}
\begin{DoxyRetVals}{Return values}
{\em 0} & on success. \\
\hline
{\em -\/1} & on failure. \\
\hline
\end{DoxyRetVals}
\hypertarget{elgamal_8h_ab91d86edb1453350a8e4023e694474ec}{
\index{elgamal.h@{elgamal.h}!elgv1vrfy@{elgv1vrfy}}
\index{elgv1vrfy@{elgv1vrfy}!elgamal.h@{elgamal.h}}
\subsubsection[{elgv1vrfy}]{\setlength{\rightskip}{0pt plus 5cm}int elgv1vrfy (
\begin{DoxyParamCaption}
\item[{const {\bf mpbarrett} $\ast$}]{p, }
\item[{const {\bf mpbarrett} $\ast$}]{n, }
\item[{const {\bf mpnumber} $\ast$}]{g, }
\item[{const {\bf mpnumber} $\ast$}]{hm, }
\item[{const {\bf mpnumber} $\ast$}]{y, }
\item[{const {\bf mpnumber} $\ast$}]{r, }
\item[{const {\bf mpnumber} $\ast$}]{s}
\end{DoxyParamCaption}
)}}
\label{elgamal_8h_ab91d86edb1453350a8e4023e694474ec}
This function performs raw ElGamal verification, variant 1.
Verifying equations:
\begin{DoxyItemize}
\item Check $0<r<p$ and $0<s<(p-1)$ \item $v_1=y^{r}r^{s}\ \textrm{mod}\ p$ \item $v_2=g^{h(m)}\ \textrm{mod}\ p$ \item Check $v_1=v_2$\end{DoxyItemize}
\begin{DoxyParams}{Parameters}
{\em p} & The prime. \\
\hline
{\em n} & The reducer mod (p-\/1). \\
\hline
{\em g} & The generator. \\
\hline
{\em hm} & The hash to be signed. \\
\hline
{\em y} & The public key value. \\
\hline
{\em r} & The signature's {\itshape r\/} value. \\
\hline
{\em s} & The signature's {\itshape s\/} value. \\
\hline
\end{DoxyParams}
\begin{DoxyRetVals}{Return values}
{\em 1} & on success. \\
\hline
{\em 0} & on failure. \\
\hline
\end{DoxyRetVals}
\hypertarget{elgamal_8h_ab5a4857d59add82a522e0c08c83298f8}{
\index{elgamal.h@{elgamal.h}!elgv3sign@{elgv3sign}}
\index{elgv3sign@{elgv3sign}!elgamal.h@{elgamal.h}}
\subsubsection[{elgv3sign}]{\setlength{\rightskip}{0pt plus 5cm}int elgv3sign (
\begin{DoxyParamCaption}
\item[{const {\bf mpbarrett} $\ast$}]{p, }
\item[{const {\bf mpbarrett} $\ast$}]{n, }
\item[{const {\bf mpnumber} $\ast$}]{g, }
\item[{{\bf randomGeneratorContext} $\ast$}]{rgc, }
\item[{const {\bf mpnumber} $\ast$}]{hm, }
\item[{const {\bf mpnumber} $\ast$}]{x, }
\item[{{\bf mpnumber} $\ast$}]{r, }
\item[{{\bf mpnumber} $\ast$}]{s}
\end{DoxyParamCaption}
)}}
\label{elgamal_8h_ab5a4857d59add82a522e0c08c83298f8}
This function performs raw ElGamal signing, variant 3.
Signing equations:
\begin{DoxyItemize}
\item $r=g^{k}\ \textrm{mod}\ p$ \item $s=xr+kh(m)\ \textrm{mod}\ (p-1)$\end{DoxyItemize}
\begin{DoxyParams}{Parameters}
{\em p} & The prime. \\
\hline
{\em n} & The reducer mod (p-\/1). \\
\hline
{\em g} & The generator. \\
\hline
{\em rgc} & The pseudo-\/random generat \\
\hline
{\em hm} & The hash to be signed. \\
\hline
{\em x} & The private key value. \\
\hline
{\em r} & The signature's {\itshape r\/} value. \\
\hline
{\em s} & The signature's {\itshape s\/} value. \\
\hline
\end{DoxyParams}
\begin{DoxyRetVals}{Return values}
{\em 0} & on success. \\
\hline
{\em -\/1} & on failure. \\
\hline
\end{DoxyRetVals}
\hypertarget{elgamal_8h_aaa1c3bb1ca269e9b40ee8a561a3f78f6}{
\index{elgamal.h@{elgamal.h}!elgv3vrfy@{elgv3vrfy}}
\index{elgv3vrfy@{elgv3vrfy}!elgamal.h@{elgamal.h}}
\subsubsection[{elgv3vrfy}]{\setlength{\rightskip}{0pt plus 5cm}int elgv3vrfy (
\begin{DoxyParamCaption}
\item[{const {\bf mpbarrett} $\ast$}]{p, }
\item[{const {\bf mpbarrett} $\ast$}]{n, }
\item[{const {\bf mpnumber} $\ast$}]{g, }
\item[{const {\bf mpnumber} $\ast$}]{hm, }
\item[{const {\bf mpnumber} $\ast$}]{y, }
\item[{const {\bf mpnumber} $\ast$}]{r, }
\item[{const {\bf mpnumber} $\ast$}]{s}
\end{DoxyParamCaption}
)}}
\label{elgamal_8h_aaa1c3bb1ca269e9b40ee8a561a3f78f6}
This function performs raw ElGamal verification, variant 3.
Verifying equations:
\begin{DoxyItemize}
\item Check $0<r<p$ and $0<s<(p-1)$ \item $v_1=g^{s}\ \textrm{mod}\ p$ \item $v_2=y^{r}r^{h(m)}\ \textrm{mod}\ p$ \item Check $v_1=v_2$\end{DoxyItemize}
\begin{DoxyParams}{Parameters}
{\em p} & The prime. \\
\hline
{\em n} & The reducer mod (p-\/1). \\
\hline
{\em g} & The generator. \\
\hline
{\em hm} & The hash to be signed. \\
\hline
{\em y} & The public key value. \\
\hline
{\em r} & The signature's {\itshape r\/} value. \\
\hline
{\em s} & The signature's {\itshape s\/} value. \\
\hline
\end{DoxyParams}
\begin{DoxyRetVals}{Return values}
{\em 1} & on success. \\
\hline
{\em 0} & on failure. \\
\hline
\end{DoxyRetVals}
