Large integer multiplication on massively parallel processors

Abstract

Results obtained by multiplying large integers using the Fermat number transform are presented. The effectiveness of the approach was previously limited by word-length constraints, which are not a factor with many new computer architectures. A convolution algorithm on a massively parallel processor, based on the Fermat number transform, is presented. Examples of the tradeoffs between modulus, interprocessor communication steps, and input size are given. The application of this algorithm in the multiplication of large integers is then discussed, and performance results on a Connection Machine are reported. The results show multiplication times ranging from about 50 ms for 2-kb integers to 2600 ms for 8-Mb integers.<>