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Communication Dans Un Congrès Année : 2001

Modular multiplication and base extensions in residue number systems

Jean-Claude Bajard
  • Fonction : Auteur
Peter Kornerup
  • Fonction : Auteur

Résumé

We present a new RNS modular multiplication for very large operands. The algorithm is based on Montgomery's (1985) method adapted to residue arithmetic. By choosing the moduli of the RNS system reasonably large, an effect corresponding to a redundant high-radix implementation is achieved, due to the carry-free nature of residue arithmetic. The actual computation in the multiplication takes place in constant time, where the unit of time is a few simple residue operations. However, it is necessary twice to convert values from one residue system into another, operations which take O(n) time on O(n) processors, where n is the number of moduli in the RNS systems. Thus these conversions are the bottlenecks of the method, and any future improvements in RNS base conversions, or the use of particular residue systems, can immediately be applied.
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Dates et versions

hal-01571103 , version 1 (01-08-2017)

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Jean-Claude Bajard, Laurent-Stéphane Didier, Peter Kornerup. Modular multiplication and base extensions in residue number systems. ARITH-15 - 15th IEEE Symposium on Computer Arithmetic, Jun 2001, Vail, CO, United States. pp.59-65, ⟨10.1109/ARITH.2001.930104⟩. ⟨hal-01571103⟩
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