Publication 1998 Issue No. 7 - July Abstract - An RNS Montgomery Modular Multiplication Algorithm
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An RNS Montgomery Modular Multiplication Algorithm
July 1998 (vol. 47 no. 7)
pp. 766-776
 ASCII Text x 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.
 BibTex x @article{ 10.1109/12.709376,author = {Jean-Claude Bajard and Laurent-Stéphane Didier and Peter Kornerup},title = {An RNS Montgomery Modular Multiplication Algorithm},journal ={IEEE Transactions on Computers},volume = {47},number = {7},issn = {0018-9340},year = {1998},pages = {766-776},doi = {http://doi.ieeecomputersociety.org/10.1109/12.709376},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - An RNS Montgomery Modular Multiplication AlgorithmIS - 7SN - 0018-9340SP766EP776EPD - 766-776A1 - Jean-Claude Bajard, A1 - Laurent-Stéphane Didier, A1 - Peter Kornerup, PY - 1998KW - Computer arithmeticKW - residue number systemKW - modular multiplicationKW - cryptography.VL - 47JA - IEEE Transactions on ComputersER -

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.

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