RNS-Based Data Representation for Handling Multiple-Precision Integers on Parallel Architectures

In most computer programs and general-purpose computing environments, the precision of any calculation is limited by the word size of the computer. However, for some applications, such as cryptography, this precision is not sufficient. In these cases, it is necessary to use multiple-precision numbers. Operations on such numbers in most computer software are implemented by third party libraries that provide data types and subroutines to store numbers with the requested precision and to perform computations. In this paper, we consider an approach for representing large integers based on the residue number system (RNS). Due to the non-positional nature of RNS, operations on multiple-precision numbers can be split into several reduced-precision operations executed in parallel. This achieves high performance and effective use of the resources of modern parallel computing architectures such as graphics processing units.