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.
Bibliographical noteCopyright 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