Fast multiplication of multiple-precision integers

Multiple-precision multiplication algorithms are of fundamental interest for both theoretical and practical reasons. The conventional method requires 0(n2) bit operations whereas the fastest known multiplication algorithm is of order 0(n log n log log n). The price that has to be paid for the increase in speed is a much more sophisticated theory and programming code. This work presents an extensive study of the best known multiple-precision multiplication algorithms. Different algorithms are implemented in C, their performance is analyzed in detail and compared to each other. The break even points, which are essential for the selection of the fastest algorithm for a particular task, are determined for a given hardware software combination