An effective New CRT based reverse converter for a novel moduli set {2&lt;sup&gt;2n&amp;#x002B;1&lt;/sup&gt; &amp;#x2212; 1, 2&lt;sup&gt;2n&amp;#x002B;1&lt;/sup&gt;, 2&lt;sup&gt;2n&lt;/sup&gt; &amp;#x2212; 1}

Bankas, Edem Kwedzo; Gbolagade, Kazeem Alagbe; Cotofana, Sorin

doi:10.1109/asap.2013.6567567

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…The Chinese Remainder Theorem is a very useful theorem used in the reverse conversion process and other operations in RNS [25]. With well selected moduli set, the CRT guarantees that a number within the legitimate range will have unique representation in RNS.…”

Section: The Chinese Remainder Theorem (Crt)mentioning

confidence: 99%

RNS Scaling Algorithm for a New Moduli Set {2^(2n+1) +1, 2^(2n+1), 2^(2n+1)-1}

Mustapha¹,

Bankas²

2017

IJCA

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Scaling is one of the difficult operations in Residue Number System (RNS) and also one of the most important units and a necessary operation used to avoid overflow in RNS based systems. In this paper, a scaling algorithm for a new moduli set {2 2n+1 +1, 2 2n+1 , 2 2n+1 -1} using the Chinese Remainder Theorem (CRT) is presented. In the design of digital systems, the goal of designers is to increase performance and decrease the amount of hardware resources. In order to achieve this, a new moduli sets is proposed to obtain a larger dynamic range and less complex hardware architecture. The CRT is further simplified for the selected moduli set to reduce the hardware complexity of the scaling algorithm. The scaling algorithm does not introduce any scaling errors and thus is efficient. When compared with the state of the art scaling algorithm using the Unit-Gate model, the results show that, the proposed scaling algorithm outperforms the state of the art scaling algorithm in terms of dynamic range (DR), area consumption, and delay by 98%, 18.4% and 21.7% respectively. General TermsModuli Set, Scaling Algorithm, Residue Number System, Chinese Remainder Theorem.

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Section: The Chinese Remainder Theorem (Crt)mentioning

confidence: 99%

RNS Scaling Algorithm for a New Moduli Set {2^(2n+1) +1, 2^(2n+1), 2^(2n+1)-1}

Mustapha¹,

Bankas²

2017

IJCA

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A residue to binary converter for a balanced moduli set {22n+1 − 1, 22n, 22n − 1}

Bankas¹,

Gbolagade²

2013

2013 International Joint Conference on Awareness Science and Technology &Amp; Ubi-Media Computing (iCAST 2013 &Amp; UMEDIA 2013

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In this paper, we propose a new moduli set 2 2n+1 − 1, 2 2n , 2 2n − 1 with its associated reverse converter. The proposed reverse converter is based on Mixed Radix Conversion (MRC). In addition to parallelizing and optimizing the MRC algorithm, the resulting architecture is further simplified in order to obtain a reverse converter that utilizes only 2 levels of Carry Save Adders and three Carry Propagate Adders. The proposed converter is purely adder based and memoryless. Our proposal has a delay of (10n + 4)tFA + 2tMUX with an area cost of (12n + 2)F As and (2n)HAs, which when expressed in terms of HA is (22n + 4), where F A, HA, and tFA represent Full Adder, Half Adder, and delay of a Full Adder, respectively. The proposed scheme is compared with state of the art similar dynamic range converters. Theoretically speaking, our proposal achieves about 62.3% hardware reduction and about 2.13% speed improvement when compared with the reverse converter for 2 n + 1, 2 n − 1, 2 2n+1 − 3, 2 2n − 2 . Also, in comaprison with the converter for 2 n − 1, 2 n + 1, 2 2n , 2 2n+1 − 1 , the results indicate that, our proposal is about 17.05% faster, but requires about 7.83% more hardware resources. Further, the area time square (Δτ 2 ) metric indicates that our proposed converter is 62.3% and 24.77% better than the state of the art reverse converters for 2 n + 1, 2 n − 1, 2 2n+1 − 3, 2 2n − 2 and 2 n − 1, 2 n + 1, 2 2n , 2 2n+1 − 1 respectively.

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A Hybrid Security Algorithm in Container-based Virtualization Environments Using Residue Number Systems

Modey,

Freeman,

Opoku-Yeboah

et al. 2024

2024 Conference on Information Communications Technology and Society (ICTAS)

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An effective New CRT based reverse converter for a novel moduli set {2<sup>2n+1</sup> − 1, 2<sup>2n+1</sup>, 2<sup>2n</sup> − 1}

Cited by 4 publications

References 14 publications

RNS Scaling Algorithm for a New Moduli Set {2^(2n+1) +1, 2^(2n+1), 2^(2n+1)-1}

RNS Scaling Algorithm for a New Moduli Set {2^(2n+1) +1, 2^(2n+1), 2^(2n+1)-1}

A residue to binary converter for a balanced moduli set {2<sup>2n+1</sup> − 1, 2<sup>2n</sup>, 2<sup>2n − 1</sup>}

A Hybrid Security Algorithm in Container-based Virtualization Environments Using Residue Number Systems

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An effective New CRT based reverse converter for a novel moduli set {2<sup>2n&#x002B;1</sup> &#x2212; 1, 2<sup>2n&#x002B;1</sup>, 2<sup>2n</sup> &#x2212; 1}

Cited by 4 publications

References 14 publications

RNS Scaling Algorithm for a New Moduli Set {2^(2n+1) +1, 2^(2n+1), 2^(2n+1)-1}

RNS Scaling Algorithm for a New Moduli Set {2^(2n+1) +1, 2^(2n+1), 2^(2n+1)-1}

A residue to binary converter for a balanced moduli set {2<sup>2n&#x002B;1</sup> &#x2212; 1, 2<sup>2n</sup>, 2<sup>2n &#x2212; 1</sup>}

A Hybrid Security Algorithm in Container-based Virtualization Environments Using Residue Number Systems

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An effective New CRT based reverse converter for a novel moduli set {2<sup>2n+1</sup> − 1, 2<sup>2n+1</sup>, 2<sup>2n</sup> − 1}

A residue to binary converter for a balanced moduli set {2<sup>2n+1</sup> − 1, 2<sup>2n</sup>, 2<sup>2n − 1</sup>}