Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures

Elliptic Curves Crypto-system (ECC) has been widely involved in many security applications. ECC computations suffer the long time inversion operation when applied using usual affine coordinates which affects the performance of ECC. Moreover, while the majority of previous researches focused on addre...

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Main Authors: Al-Khatib, Mohammad Hussein Fayiz, Jaafar, Azmi, Ahmad Zukarnain, Zuriati, Md. Said, Mohamad Rushdan
Format: Article
Language:English
Published: Praise Worthy Prize 2011
Online Access:http://psasir.upm.edu.my/id/eprint/22502/1/Trade-off%20between%20area%20and%20speed%20for%20projective%20Edwards%20Elliptic%20Curves%20Crypto-system%20over%20GF%20%28p%29%20using%20parallel%20hardware%20designs%20and%20architectures.pdf
http://psasir.upm.edu.my/id/eprint/22502/
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Institution: Universiti Putra Malaysia
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spelling my.upm.eprints.225022015-10-09T07:40:15Z http://psasir.upm.edu.my/id/eprint/22502/ Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures Al-Khatib, Mohammad Hussein Fayiz Jaafar, Azmi Ahmad Zukarnain, Zuriati Md. Said, Mohamad Rushdan Elliptic Curves Crypto-system (ECC) has been widely involved in many security applications. ECC computations suffer the long time inversion operation when applied using usual affine coordinates which affects the performance of ECC. Moreover, while the majority of previous researches focused on addressing the performance of ECC, other factors that play crucial role in building efficient ECC design for different security applications have not been intensively investigated, such as area, system utilization, resources-consuming, AT, and AT2 cost factors. Our research proposes several designs and architectures for Edwards ECC over GF (p) using projective coordinates (X/Z2 Y/Z2). All our proposed designs apply ECC computations with no inversion operation. To improve the performance even further, our research utilizes the inherent parallelism in elliptic curves computations by applying arithmetic operations for ECC in parallel. Our results show that the performance for the proposed 5-PM design overcomes designs using the known projective coordinates as well as the affine coordinates, since it achieves the shortest time delay. Furthermore, the other proposed designs provide an attractive trade-off between mentioned factors by varying the degree of parallelism for ECC computational schemes. Although this trade-off compromises the performance of ECC, the other factors were enhanced progressively. This helps to select the most suitable ECC design for several elliptic curves applications according to their requirements and available resources. The 2-PM design obtains the best system utilization results and AT cost with less area in comparison with designs using a higher degree of parallelism. Praise Worthy Prize 2011-07 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/22502/1/Trade-off%20between%20area%20and%20speed%20for%20projective%20Edwards%20Elliptic%20Curves%20Crypto-system%20over%20GF%20%28p%29%20using%20parallel%20hardware%20designs%20and%20architectures.pdf Al-Khatib, Mohammad Hussein Fayiz and Jaafar, Azmi and Ahmad Zukarnain, Zuriati and Md. Said, Mohamad Rushdan (2011) Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures. International Review on Computers and Software, 6 (4). pp. 615-625. ISSN 1828-6003; ESSN: 1828-6011
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Elliptic Curves Crypto-system (ECC) has been widely involved in many security applications. ECC computations suffer the long time inversion operation when applied using usual affine coordinates which affects the performance of ECC. Moreover, while the majority of previous researches focused on addressing the performance of ECC, other factors that play crucial role in building efficient ECC design for different security applications have not been intensively investigated, such as area, system utilization, resources-consuming, AT, and AT2 cost factors. Our research proposes several designs and architectures for Edwards ECC over GF (p) using projective coordinates (X/Z2 Y/Z2). All our proposed designs apply ECC computations with no inversion operation. To improve the performance even further, our research utilizes the inherent parallelism in elliptic curves computations by applying arithmetic operations for ECC in parallel. Our results show that the performance for the proposed 5-PM design overcomes designs using the known projective coordinates as well as the affine coordinates, since it achieves the shortest time delay. Furthermore, the other proposed designs provide an attractive trade-off between mentioned factors by varying the degree of parallelism for ECC computational schemes. Although this trade-off compromises the performance of ECC, the other factors were enhanced progressively. This helps to select the most suitable ECC design for several elliptic curves applications according to their requirements and available resources. The 2-PM design obtains the best system utilization results and AT cost with less area in comparison with designs using a higher degree of parallelism.
format Article
author Al-Khatib, Mohammad Hussein Fayiz
Jaafar, Azmi
Ahmad Zukarnain, Zuriati
Md. Said, Mohamad Rushdan
spellingShingle Al-Khatib, Mohammad Hussein Fayiz
Jaafar, Azmi
Ahmad Zukarnain, Zuriati
Md. Said, Mohamad Rushdan
Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures
author_facet Al-Khatib, Mohammad Hussein Fayiz
Jaafar, Azmi
Ahmad Zukarnain, Zuriati
Md. Said, Mohamad Rushdan
author_sort Al-Khatib, Mohammad Hussein Fayiz
title Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures
title_short Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures
title_full Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures
title_fullStr Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures
title_full_unstemmed Trade-off between area and speed for projective Edwards Elliptic Curves Crypto-system over GF (p) using parallel hardware designs and architectures
title_sort trade-off between area and speed for projective edwards elliptic curves crypto-system over gf (p) using parallel hardware designs and architectures
publisher Praise Worthy Prize
publishDate 2011
url http://psasir.upm.edu.my/id/eprint/22502/1/Trade-off%20between%20area%20and%20speed%20for%20projective%20Edwards%20Elliptic%20Curves%20Crypto-system%20over%20GF%20%28p%29%20using%20parallel%20hardware%20designs%20and%20architectures.pdf
http://psasir.upm.edu.my/id/eprint/22502/
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