ABSTRACT
<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>
INDEX TERMS
Computer arithmetic, residue number system, modular multiplication, cryptography.
CITATION

J. Bajard, L. Didier and P. Kornerup, "An RNS Montgomery Modular Multiplication Algorithm," in IEEE Transactions on Computers, vol. 47, no. , pp. 766-776, 1998.
doi:10.1109/12.709376
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