An RNS Montgomery modular multiplication algorithm
Jean-Claude Bajard, Laurent-Stéphane Didier, Peter Kornerup · IEEE Transactions on Computers · 1998
We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's method adapted to mixed radix, and is performed using a residue number system. By choosing the moduli of the RNS system reasonably large and implementing the system on a ring of fairly simple processors, an effect corresponding to a redundant high-radix implementation is achieved. The algorithm can be implemented to run in O(n) time on O(n) processors, where n is the number of moduli in the RNS system, and the unit of time is a simple residue operation, possibly by table look-up. Two different implementations are proposed, one based on processors attached to a broadcast bus, another on an oriented ring structure.