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add documentation of mp_expt_d_ex()

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Steffen Jaeckel 2014-10-10 19:49:40 +02:00 committed by Tom St Denis
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bn.tex
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@ -1546,12 +1546,29 @@ slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery
\chapter{Exponentiation}
\section{Single Digit Exponentiation}
\index{mp\_expt\_d\_ex}
\begin{alltt}
int mp_expt_d_ex (mp_int * a, mp_digit b, mp_int * c, int fast)
\end{alltt}
This function computes $c = a^b$.
With parameter \textit{fast} set to $0$ the old version of the algorithm is used,
when \textit{fast} is $1$, a faster but not statically timed version of the algorithm is used.
The old version uses a simple binary left-to-right algorithm.
It is faster than repeated multiplications by $a$ for all values of $b$ greater than three.
The new version uses a binary right-to-left algorithm.
The difference between the old and the new version is that the old version always
executes $DIGIT\_BIT$ iterations. The new algorithm executes only $n$ iterations
where $n$ is equal to the position of the highest bit that is set in $b$.
\index{mp\_expt\_d}
\begin{alltt}
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
\end{alltt}
This computes $c = a^b$ using a simple binary left-to-right algorithm. It is faster than repeated multiplications by
$a$ for all values of $b$ greater than three.
mp\_expt\_d(a, b, c) is a wrapper function to mp\_expt\_d\_ex(a, b, c, 0).
\section{Modular Exponentiation}
\index{mp\_exptmod}