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Conference Papers Year : 2009

Selected RNS Bases for Modular Multiplication

Jean-Claude Bajard
Marcelo Kaihara
  • Function : Author
  • PersonId : 861192
Thomas Plantard
  • Function : Author
  • PersonId : 861193


The selection of the elements of the bases in an RNS modular multiplication method is crucial and has a great impact in the overall performance. This work proposes specific sets of optimal RNS moduli with elements of Hamming weight three whose inverses used in the MRS reconstruction have very small Hamming weight. This property is exploited in RNS bases conversions, to completely remove and replace the products by few additions/subtractions and shifts, reducing the time complexity of modular multiplication. These bases are specially crafted to computation with operands of sizes 256 or more and are suitable for cryptographic applications such as the ECC protocols.

Dates and versions

lirmm-00394985 , version 1 (13-06-2009)



Jean-Claude Bajard, Marcelo Kaihara, Thomas Plantard. Selected RNS Bases for Modular Multiplication. ARITH'2009: 19th Symposium on Computer Arithmetic, Jun 2009, Portland, Oregon, United States. pp.25-35, ⟨10.1109/ARITH.2009.20⟩. ⟨lirmm-00394985⟩
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