hcrypto/libtommath/tommath.tex

362 $O(n^k)$ for $n, k \in \Z^{+}$.  This will help make useful comparisons in terms of the speed of the algorithms and how
442 even though this library is written entirely in ISO C, considerable care has been taken to optimize the algorithm implementations within the
480 When compiled with GCC for the x86 processor and optimized for speed the entire library is approximately $100$KiB\footnote{The notation ``KiB'' means $2^{10}$ octets, similarly ``MiB'' means $2^{20}$ octets.}
1103 \begin{tabular}{cl}
1222 as a compiler may optimize out the redundant pointer operations.  However, there are two dominant reasons to use aliases.
1224 The first reason is that most compilers will not effectively optimize pointer arithmetic.  For example, some optimizations
1227 aliases optimize the code considerably before the compiler even reads the source code which means the end compiled code
1607 \begin{tabular}{cl}
1613 $\left [ 1 \right ]$ & Suggest a simple method to speed up the implementation of mp\_cmp\_mag based  \\
2321 complete.  It is possible to optimize this algorithm down to a $O(n)$ algorithm at a cost of making the algorithm slightly harder to follow.
2450 \begin{tabular}{cl}
2798 the speed increase is actually much more.  With $O(n)$ space the algorithm can be reduced to $O(pn + qn)$ time by implementing the $n$ multiply
2943 making it an ideal algorithm to speed up certain public key cryptosystems such as RSA and Diffie-Hellman.
3573 \begin{tabular}{cl}
3629 It would take another common optimization to optimize the algorithm.
3632 The trick used to optimize the above equation is based on a technique of emulating floating point data types with fixed precision integers.  Fixed
3633 point arithmetic would become very popular as it greatly optimize the ``3d-shooter'' genre of games in the mid 1990s when floating point units were
4140 the speed of the algorithm.
4686 modular exponentiation to greatly speed up the operation.
4691 \begin{tabular}{cl}
4708 such cryptosystem and many methods have been sought to speed it up.
4733 While this current method is a considerable speed up there are further improvements to be made.  For example, the $a^{2^i}$ term does not need to