From eca442b01d1c1aa229413e14c75cbb2c5c413caa Mon Sep 17 00:00:00 2001
From: Steffen Jaeckel <s@jaeckel.eu>
Date: Fri, 10 Oct 2014 19:49:40 +0200
Subject: [PATCH] add documentation of mp_expt_d_ex()

---
 bn.tex | 21 +++++++++++++++++++--
 1 file changed, 19 insertions(+), 2 deletions(-)

diff --git a/bn.tex b/bn.tex
index 3ae7664..d17c793 100644
--- a/bn.tex
+++ b/bn.tex
@@ -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}