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fix doc/bn.tex

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Steffen Jaeckel 2018-12-26 15:48:12 +01:00
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doc/bn.tex
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@ -1168,7 +1168,7 @@ It is also not very uncommon to need just the power of two $2^b$; for example t
\begin{alltt} \begin{alltt}
int mp_2expt(mp_int *a, int b); int mp_2expt(mp_int *a, int b);
\end{alltt} \end{alltt}
It is faster than doing it by shifting $1$ with \texttt{mp_mul_2d}. It is faster than doing it by shifting $1$ with \texttt{mp\_mul\_2d}.
\subsection{Polynomial Basis Operations} \subsection{Polynomial Basis Operations}
@ -1680,23 +1680,23 @@ slower than mp\_dr\_reduce but faster for most moduli sizes than the Montgomery
Some of the combinations of an arithmetic operations followed by a modular reduction can be done in a faster way. The ones implemented are: Some of the combinations of an arithmetic operations followed by a modular reduction can be done in a faster way. The ones implemented are:
Addition $d = (a + b) \mod c$ Addition $d = (a + b) \mod c$
\index{mp\_addmod} \index{mp\_addmod}
\begin{alltt} \begin{alltt}
int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
\end{alltt} \end{alltt}
Subtraction $d = (a - b) \mod c$ Subtraction $d = (a - b) \mod c$
\begin{alltt} \begin{alltt}
int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
\end{alltt} \end{alltt}
Multiplication $d = (ab) \mod c$ Multiplication $d = (ab) \mod c$
\begin{alltt} \begin{alltt}
int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
\end{alltt} \end{alltt}
Squaring $d = (a^2) \mod c$ Squaring $d = (a^2) \mod c$
\begin{alltt} \begin{alltt}
int mp_sqrmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); int mp_sqrmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d);
\end{alltt} \end{alltt}
@ -1745,7 +1745,7 @@ moduli of the a ``restricted diminished radix'' form lead to the fastest modular
and the other two algorithms. and the other two algorithms.
\section{Modulus a Power of Two} \section{Modulus a Power of Two}
\index{mp\_mod_2d} \index{mp\_mod\_2d}
\begin{alltt} \begin{alltt}
int mp_mod_2d(const mp_int *a, int b, mp_int *c) int mp_mod_2d(const mp_int *a, int b, mp_int *c)
\end{alltt} \end{alltt}
@ -1825,7 +1825,7 @@ require ten tests whereas a 1024-bit number would only require four tests.
You should always still perform a trial division before a Miller-Rabin test though. You should always still perform a trial division before a Miller-Rabin test though.
A small table, broke in two for typographical reasons, with the number of rounds of Miller-Rabin tests is shown below. A small table, broke in two for typographical reasons, with the number of rounds of Miller-Rabin tests is shown below.
The first column is the number of bits $b$ in the prime $p = 2^b$, the numbers in the first row represent the The first column is the number of bits $b$ in the prime $p = 2^b$, the numbers in the first row represent the
probability that the number that all of the Miller-Rabin tests deemed a pseudoprime is actually a composite. There is a deterministic test for numbers smaller than $2^{80}$. probability that the number that all of the Miller-Rabin tests deemed a pseudoprime is actually a composite. There is a deterministic test for numbers smaller than $2^{80}$.
\begin{table}[h] \begin{table}[h]
@ -2009,7 +2009,8 @@ int mp_rand(mp_int *a, int digits)
\end{alltt} \end{alltt}
The function generates a random number of \texttt{digits} bits. The function generates a random number of \texttt{digits} bits.
This random number is cryptographically secure if the source of random numbers the operating systems offers is cryptographically secure. It will use \texttt{arc4random()} if the OS is a BSD flavor, Wincrypt on Windows, and \texttt{\dev\urandom} on all operating systems that have it. This random number is cryptographically secure if the source of random numbers the operating systems offers is cryptographically secure.
It will use \texttt{arc4random()} if the OS is a BSD flavor, Wincrypt on Windows, and \texttt{\\dev\\urandom} on all operating systems that have it.
\chapter{Input and Output} \chapter{Input and Output}