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Keywords = sum of residues (SOR) reduction

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16 pages, 914 KiB  
Article
Improved Sum of Residues Modular Multiplication Algorithm
by Mohamad Ali Mehrabi
Cryptography 2019, 3(2), 14; https://doi.org/10.3390/cryptography3020014 - 29 May 2019
Cited by 6 | Viewed by 7681
Abstract
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 [...] Read more.
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. Full article
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