Improved sum of residues modular multiplication algorithm

Mohamad Ali Mehrabi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
26 Downloads (Pure)


Modular reduction of large values is a core operation in most common public-key cryptosystems that involves intensive computations in finite fields. Within such schemes, efficiency is a critical issue for the effectiveness of practical implementation of modular reduction. Recently, Residue Number Systems have drawn attention in cryptography application as they provide a good means for extreme long integer arithmetic and their carry-free operations make parallel implementation feasible. In this paper, we present an algorithm to calculate the precise value of “ X mod p ”directly in the RNS representation of an integer. The pipe-lined, non-pipe-lined, and parallel hardware architectures are proposed and implemented on XILINX FPGAs.
Original languageEnglish
Article number14
Pages (from-to)1-16
Number of pages16
Issue number2
Publication statusPublished - Jun 2019

Bibliographical note

Copyright the Author(s) 2019. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • modular reduction
  • modular multiplication
  • residue number systems (RNS)
  • Elliptic Curve Cryptography (ECC)
  • sum of residues (SOR) reduction
  • montgomery modular reduction (MMR)
  • Residue number systems (RNS)
  • Modular multiplication
  • Modular reduction
  • Montgomery modular reduction (MMR)
  • Sum of residues (SOR) reduction


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