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<p><b>Abstract</b>—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 <tmath>${\cal O}(n)$</tmath> time on <tmath>${\cal O}(n)$</tmath> processors, where <it>n</it> 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.</p>
Computer arithmetic, residue number system, modular multiplication, cryptography.
Jean-Claude Bajard, Laurent-Stéphane Didier, Peter Kornerup, "An RNS Montgomery Modular Multiplication Algorithm", IEEE Transactions on Computers, vol. 47, no. , pp. 766-776, July 1998, doi:10.1109/12.709376
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