Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields

Ibrahim Hazmi; Fayez Gebali; Atef Ibrahim

doi:10.1109/CCECE.2019.8861557

Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields

Ibrahim Hazmi
, Fayez Gebali
, Atef Ibrahim

Computer Engineering

University of Victoria BC

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Hardware implementation of the extended Euclidean algorithm (EEA) over ternary field introduces many challenges, include degree evaluations during and after each iteration of the algorithm. This paper presents a novel realization of the traditional EEA over ternary fields in a concurrent manner, resolving the issues stated above by using a former systolic architectural approach. Polynomial division and multiplication in GF(3m) are performed concurrently. Accordingly, an EEA-based ternary inverter is built. Then, the complexity of the proposed inverter is analyzed in comparison with efficient designs in the literature, concluding that our design has the lowest area-time complexity.

Original language	English
Title of host publication	2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781728103198
DOIs	https://doi.org/10.1109/CCECE.2019.8861557
State	Published - May 2019
Event	2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019 - Edmonton, Canada Duration: 5 May 2019 → 8 May 2019

Publication series

Name	2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019

Conference

Conference	2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019
Country/Territory	Canada
City	Edmonton
Period	5/05/19 → 8/05/19

Keywords

Concurrent Extended Euclidean Algorithm (EEA)
Systolic Array
Ternary Fields Inversion

Access to Document

10.1109/CCECE.2019.8861557

Cite this

Hazmi, I., Gebali, F., & Ibrahim, A. (2019). Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields. In 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019 Article 8861557 (2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CCECE.2019.8861557

Hazmi, Ibrahim ; Gebali, Fayez ; Ibrahim, Atef. / Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields. 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019. Institute of Electrical and Electronics Engineers Inc., 2019. (2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019).

@inproceedings{480e0ca0ce554f81abd14fc1be8d65fe,

title = "Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields",

abstract = "Hardware implementation of the extended Euclidean algorithm (EEA) over ternary field introduces many challenges, include degree evaluations during and after each iteration of the algorithm. This paper presents a novel realization of the traditional EEA over ternary fields in a concurrent manner, resolving the issues stated above by using a former systolic architectural approach. Polynomial division and multiplication in GF(3m) are performed concurrently. Accordingly, an EEA-based ternary inverter is built. Then, the complexity of the proposed inverter is analyzed in comparison with efficient designs in the literature, concluding that our design has the lowest area-time complexity.",

keywords = "Concurrent Extended Euclidean Algorithm (EEA), Systolic Array, Ternary Fields Inversion",

author = "Ibrahim Hazmi and Fayez Gebali and Atef Ibrahim",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019 ; Conference date: 05-05-2019 Through 08-05-2019",

year = "2019",

month = may,

doi = "10.1109/CCECE.2019.8861557",

language = "English",

series = "2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019",

address = "United States",

}

Hazmi, I, Gebali, F & Ibrahim, A 2019, Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields. in 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019., 8861557, 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019, Institute of Electrical and Electronics Engineers Inc., 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019, Edmonton, Canada, 5/05/19. https://doi.org/10.1109/CCECE.2019.8861557

Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields. / Hazmi, Ibrahim; Gebali, Fayez; Ibrahim, Atef.
2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8861557 (2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields

AU - Hazmi, Ibrahim

AU - Gebali, Fayez

AU - Ibrahim, Atef

PY - 2019/5

Y1 - 2019/5

N2 - Hardware implementation of the extended Euclidean algorithm (EEA) over ternary field introduces many challenges, include degree evaluations during and after each iteration of the algorithm. This paper presents a novel realization of the traditional EEA over ternary fields in a concurrent manner, resolving the issues stated above by using a former systolic architectural approach. Polynomial division and multiplication in GF(3m) are performed concurrently. Accordingly, an EEA-based ternary inverter is built. Then, the complexity of the proposed inverter is analyzed in comparison with efficient designs in the literature, concluding that our design has the lowest area-time complexity.

AB - Hardware implementation of the extended Euclidean algorithm (EEA) over ternary field introduces many challenges, include degree evaluations during and after each iteration of the algorithm. This paper presents a novel realization of the traditional EEA over ternary fields in a concurrent manner, resolving the issues stated above by using a former systolic architectural approach. Polynomial division and multiplication in GF(3m) are performed concurrently. Accordingly, an EEA-based ternary inverter is built. Then, the complexity of the proposed inverter is analyzed in comparison with efficient designs in the literature, concluding that our design has the lowest area-time complexity.

KW - Concurrent Extended Euclidean Algorithm (EEA)

KW - Systolic Array

KW - Ternary Fields Inversion

UR - https://www.scopus.com/pages/publications/85074095705

U2 - 10.1109/CCECE.2019.8861557

DO - 10.1109/CCECE.2019.8861557

M3 - Conference contribution

AN - SCOPUS:85074095705

T3 - 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019

BT - 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019

Y2 - 5 May 2019 through 8 May 2019

ER -

Hazmi I, Gebali F, Ibrahim A. Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields. In 2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019. Institute of Electrical and Electronics Engineers Inc. 2019. 8861557. (2019 IEEE Canadian Conference of Electrical and Computer Engineering, CCECE 2019). doi: 10.1109/CCECE.2019.8861557

Implementation of High Speed and Low Area Extended Euclidean Inversion over Ternary Fields

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this