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An RNS Montgomery Modular Multiplication Algorithm
July 1998 (vol. 47 no. 7)
pp. 766-776

Abstract—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 ${\cal O}(n)$ time on ${\cal O}(n)$ 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.

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Index Terms:
Computer arithmetic, residue number system, modular multiplication, cryptography.
Citation:
Jean-Claude Bajard, Laurent-Stéphane Didier, Peter Kornerup, "An RNS Montgomery Modular Multiplication Algorithm," IEEE Transactions on Computers, vol. 47, no. 7, pp. 766-776, July 1998, doi:10.1109/12.709376
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