Large Integer Multiplication (LIM) Part 1

Large Integer Multiplication is an algorithm to multiply two large integers together efficiently.
This is often used by factorization algorithms, both for exponentiation, for example - when it is combined with the Russian Peasant method for extra speed (see earlier) or in fact, often, for division (by multiplying by the inverse of a number as the dividend)
"Long Multiplication" is the obvious, and naive, method, but the time complexity of this is of order n^2 for two n-digit integers. So a number of improvements have been suggested. These will be examined in later parts of this series. For the moment read all about LIM on Wikipedia:
http://en.wikipedia.org/wiki/Multiplication_algorithm