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28 \def\Or{{\rm\ or\ }}
245 Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
248 source code is also accessible for computer science students attempting to learn ``BigNum'' or multiple precision
284 So it may feel tempting to just rip the math code out of GnuPG (or GnuMP where it was taken from originally) in your
351 hold the structure itself by yourself (whether off stack or heap it doesn't matter). The very first thing that must be
442 variables in an ``all or nothing'' fashion. That is, they are either all initialized successfully or they are all
972 Logical operations are operations that can be performed either with simple shifts or boolean operators such as
973 AND, XOR and OR directly. These operations are very quick.
977 Multiplications and divisions by any power of two can be performed with quick logical shifts either left or
980 When multiplying or dividing by two a special case routine can be used which are as follows.
1050 This will multiply $a$ by $2^b$ and store the result in ``c''. If the value of $b$ is less than or equal to
1088 \subsection{AND, OR and XOR Operations}
1090 While AND, OR and XOR operations are not typical ``bignum functions'' they can be useful in several instances. The
1100 Which compute $c = a \odot b$ where $\odot$ is one of OR, AND or XOR.
1104 To compute an addition or subtraction the following two functions can be used.
1112 Which perform $c = a \odot b$ where $\odot$ is one of signed addition or subtraction. The operations are fully sign
1146 $bc + d = a$. Note that either of $c$ or $d$ can be set to \textbf{NULL} if their value is not required. If
1234 multiplications with Toom-Cook or 100,000,000 single precision multiplications with the standard Comba (a factor
1237 So why not always use Karatsuba or Toom-Cook? The simple answer is that they have so much overhead that they're not
1408 Which calculates $a = R$ for the odd moduli $b$ without using multiplication or division.
1519 Since the moduli are restricted this algorithm is not particularly useful for something like Rabin, RSA or
1585 $a^{1/16}$ is equivalent to $\left (a^{1/4} \right)^{1/4}$ or simply
1605 equal to $b$ or not. If the values are equal then $a$ is probably prime and $result$ is set to one. Otherwise $result$
1622 or so unique bases. However, it has been proven that the probability of failure goes down as the size of the input goes up.
1629 This returns the number of trials required for a $2^{-96}$ (or lower) probability of failure for a given ``size'' expressed
1658 This will find a prime greater than $256^{size}$ which can be ``bbs\_style'' or not depending on $bbs$ and must pass
1682 (see fig. \ref{fig:primeopts}) which can be OR'ed together. The callback parameters are used as in
1747 This will store $a$ into the buffer $b$ in big--endian format. Fortunately this is exactly what DER (or is it ASN?)
1765 They operate essentially the same as the unsigned copies except they prefix the data with zero or non--zero
1831 an entire mp\_int to store a number like $1$ or $2$.