Selected application of the Chinese Remainder Theorem in multiparty computation

Jakubski, Artur

doi:10.17512/jamcm.2016.1.04

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…k are calculated in accordance with (13) and (14), respectively. The proof of this theorem follows directly from Equations (7)- (14).…”

Section: Rank Calculation In Minimally Redundant Rnsmentioning

confidence: 99%

“…k are calculated in accordance with (13) and (14), respectively. The proof of this theorem follows directly from Equations (7)- (14). According to Theorem 2, the transition from non-redundant to minimally redundant residue coding allows replacing rank correction ∆ k (X) requiring time-consuming calculations by a trivially calculated two-value attribute δ k (X) ∈ {0, 1} in (3).…”

Section: Rank Calculation In Minimally Redundant Rnsmentioning

confidence: 99%

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An efficient implementation of the Chinese Remainder Theorem in minimally redundant Residue Number System

Selianinau

2020

csci

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The Chinese Remainder Theorem (CRT) widely used in many modern computer applications. This paper presents an efficient approach to the calculation of the rank of a number, a principal positional characteristic used in the Residue Number System (RNS). The proposed method does not use large modulo addition operations compared to a straightforward implementation of the CRT algorithm. The rank of a number is equal to a sum of an inexact rank and a two-valued correction factor that only takes on the values 0 or 1. We propose a minimally redundant RNS, which provides low computational complexity of the rank calculation. The effectiveness of the novel method is analyzed concerning conventional non-redundant RNS. Owing to the extension of the residue code, by adding the extra residue modulo 2, the complexity of rank calculation goes down from \(O(k^2)\) to \(O(k)\), where \(k\) equals the number of residues in non-redundant RNS.

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“…k are calculated in accordance with (13) and (14), respectively. The proof of this theorem follows directly from Equations (7)- (14).…”

Section: Rank Calculation In Minimally Redundant Rnsmentioning

confidence: 99%