diff --git a/doc/bn.tex b/doc/bn.tex index 7050b3f..79ae8a4 100644 --- a/doc/bn.tex +++ b/doc/bn.tex @@ -1168,7 +1168,7 @@ It is also not very uncommon to need just the power of two $2^b$; for example t \begin{alltt} int mp_2expt(mp_int *a, int b); \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} @@ -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: -Addition $d = (a + b) \mod c$ +Addition $d = (a + b) \mod c$ \index{mp\_addmod} \begin{alltt} int mp_addmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); \end{alltt} -Subtraction $d = (a - b) \mod c$ +Subtraction $d = (a - b) \mod c$ \begin{alltt} int mp_submod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); \end{alltt} -Multiplication $d = (ab) \mod c$ +Multiplication $d = (ab) \mod c$ \begin{alltt} int mp_mulmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); \end{alltt} -Squaring $d = (a^2) \mod c$ +Squaring $d = (a^2) \mod c$ \begin{alltt} int mp_sqrmod(const mp_int *a, const mp_int *b, const mp_int *c, mp_int *d); \end{alltt} @@ -1745,7 +1745,7 @@ moduli of the a ``restricted diminished radix'' form lead to the fastest modular and the other two algorithms. \section{Modulus a Power of Two} -\index{mp\_mod_2d} +\index{mp\_mod\_2d} \begin{alltt} int mp_mod_2d(const mp_int *a, int b, mp_int *c) \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. 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 $2^{80}$. \begin{table}[h] @@ -2009,7 +2009,8 @@ int mp_rand(mp_int *a, int digits) \end{alltt} 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}