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BigNum Math: Implementing Cryptographic Multiple Precision Arithmetic

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The origins of this book are part of an interesting period of my life. A period that
saw me move from a shy and disorganized young adult, into a software developer
who has toured various parts of the world, and met countless new friends and
colleagues. It all began in December of 2001, nearly five years ago. I started a
project that would later become known as LibTomCrypt, and be used by devel-
opers throughout industry worldwide.

The LibTomCrypt project was originally started as a way to focus my energies
on to something constructive, while also learning new skills. The first year of the
project taught me quite a bit about how to organize a product, document and
support it and maintain it over time. Around the winter of 2002 I was seeking
another project to spread my time with. Realizing that the math performance of
LibTomCrypt was lacking, I set out to develop a new math library.

Hence, the LibTomMath project was born. It was originally merely a set of
patches against an existing project that quickly grew into a project of its own.
Writing the math library from scratch was fundamental to producing a stable and
independent product. It also taught me what sort of algorithms are available to
do operations such as modular exponentiation. The library became fairly stable
and reliable after only a couple of months of development and was immediately
put to use.

In the summer of 2003, I was yet again looking for another project to grow
into. Realizing that merely implementing the math routines is not enough to
truly understand them, I set out to try and explain them myself. In doing so, I
eventually mastered the concepts behind the algorithms. This knowledge is what
I hope will be passed on to the reader. This text is actually derived from the
public domain archives I maintain on my www.libtomcrypt.com Web site.
(HTML tags aren't allowed.)

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