The authors 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 an a ring of fairly simple processors, an effect corresponding to a redundant high-radix implementation is achieved. The algorithm call 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.