High-Performance FPGA Implementation of Modular Inversion over F256 for Elliptic Curve Cryptography

Md Selim Hossain; Yinan Kong

doi:10.1109/DSDIS.2015.47

High-Performance FPGA Implementation of Modular Inversion over F₂₅₆ for Elliptic Curve Cryptography

Md Selim Hossain, Yinan Kong

School of Engineering

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

25 Citations (Scopus)

Abstract

Modular Inversion over a prime field is an important operation for public-key cryptographic applications. It is the most crucial operation to speed up the calculation of an elliptic curve crypto-processor (ECC) when affine coordinates are used. In this work, the main goal is to implement a fast, high-performance modular inversion for ECC using field-programmable gate-array (FPGA) technology. A binary inversion algorithm in VHDL has been used for this efficient implementation. Timing simulation shows that the delay for one modular inversion operation in a modern Xilinx Virtex-7 FPGA is only 2.329 μs at the maximum frequency of 146.389 MHz. We have implemented an area-efficient design which takes a small amount of resources on the FPGA and needs only 1480 slices. To the best of the authors' knowledge, the proposed modular inversion over F₂₅₆ provides a better performance than the available hardware implementations in terms of the area and the timing.

Original language	English
Title of host publication	Proceedings
Subtitle of host publication	2015 IEEE international conference on data science and data intensive systems; the eighth IEEE international conference cyber, physical and social computing; the eleventh IEEE international conference on green computing and communications and the eighth IEEE international conference on internet of things
Editors	Jinjun Chen, Laurence T. Yang
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	169-174
Number of pages	6
ISBN (Electronic)	9781509002146
DOIs	https://doi.org/10.1109/DSDIS.2015.47
Publication status	Published - 2015
Event	2015 IEEE International Conference on Data Science and Data Intensive Systems; 8th IEEE International Conference Cyber, Physical and Social Computing; 11th IEEE International Conference on Green Computing and Communications and 8th IEEE International Conference on Internet of Things, DSDIS/CPSCom/GreenCom/iThings 2015 - Sydney, Australia Duration: 11 Dec 2015 → 13 Dec 2015

Other

Other	2015 IEEE International Conference on Data Science and Data Intensive Systems; 8th IEEE International Conference Cyber, Physical and Social Computing; 11th IEEE International Conference on Green Computing and Communications and 8th IEEE International Conference on Internet of Things, DSDIS/CPSCom/GreenCom/iThings 2015
Country/Territory	Australia
City	Sydney
Period	11/12/15 → 13/12/15

Keywords

Elliptic curve cryptography (ECC)
field-programmable gate-array (FPGA)
modular inversion (MI)
NIST (National Institute of Standards and Technology) prime field
publickey cryptography (PKC)

Access to Document

10.1109/DSDIS.2015.47

Cite this

Hossain, M. S., & Kong, Y. (2015). High-Performance FPGA Implementation of Modular Inversion over F₂₅₆ for Elliptic Curve Cryptography. In J. Chen, & L. T. Yang (Eds.), Proceedings: 2015 IEEE international conference on data science and data intensive systems; the eighth IEEE international conference cyber, physical and social computing; the eleventh IEEE international conference on green computing and communications and the eighth IEEE international conference on internet of things (pp. 169-174). Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/DSDIS.2015.47

Hossain, Md Selim ; Kong, Yinan. / High-Performance FPGA Implementation of Modular Inversion over F₂₅₆ for Elliptic Curve Cryptography. Proceedings: 2015 IEEE international conference on data science and data intensive systems; the eighth IEEE international conference cyber, physical and social computing; the eleventh IEEE international conference on green computing and communications and the eighth IEEE international conference on internet of things. editor / Jinjun Chen ; Laurence T. Yang. Piscataway, NJ : Institute of Electrical and Electronics Engineers (IEEE), 2015. pp. 169-174

@inproceedings{eece99c913854790b3c0c89a0f9f2d9d,

title = "High-Performance FPGA Implementation of Modular Inversion over F256 for Elliptic Curve Cryptography",

abstract = "Modular Inversion over a prime field is an important operation for public-key cryptographic applications. It is the most crucial operation to speed up the calculation of an elliptic curve crypto-processor (ECC) when affine coordinates are used. In this work, the main goal is to implement a fast, high-performance modular inversion for ECC using field-programmable gate-array (FPGA) technology. A binary inversion algorithm in VHDL has been used for this efficient implementation. Timing simulation shows that the delay for one modular inversion operation in a modern Xilinx Virtex-7 FPGA is only 2.329 μs at the maximum frequency of 146.389 MHz. We have implemented an area-efficient design which takes a small amount of resources on the FPGA and needs only 1480 slices. To the best of the authors' knowledge, the proposed modular inversion over F256 provides a better performance than the available hardware implementations in terms of the area and the timing.",

keywords = "Elliptic curve cryptography (ECC), field-programmable gate-array (FPGA), modular inversion (MI), NIST (National Institute of Standards and Technology) prime field, publickey cryptography (PKC)",

author = "Hossain, \{Md Selim\} and Yinan Kong",

year = "2015",

doi = "10.1109/DSDIS.2015.47",

language = "English",

pages = "169--174",

editor = "Jinjun Chen and Yang, \{Laurence T.\}",

booktitle = "Proceedings",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

address = "United States",

note = "2015 IEEE International Conference on Data Science and Data Intensive Systems; 8th IEEE International Conference Cyber, Physical and Social Computing; 11th IEEE International Conference on Green Computing and Communications and 8th IEEE International Conference on Internet of Things, DSDIS/CPSCom/GreenCom/iThings 2015 ; Conference date: 11-12-2015 Through 13-12-2015",

}

Hossain, MS & Kong, Y 2015, High-Performance FPGA Implementation of Modular Inversion over F₂₅₆ for Elliptic Curve Cryptography. in J Chen & LT Yang (eds), Proceedings: 2015 IEEE international conference on data science and data intensive systems; the eighth IEEE international conference cyber, physical and social computing; the eleventh IEEE international conference on green computing and communications and the eighth IEEE international conference on internet of things. Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, pp. 169-174, 2015 IEEE International Conference on Data Science and Data Intensive Systems; 8th IEEE International Conference Cyber, Physical and Social Computing; 11th IEEE International Conference on Green Computing and Communications and 8th IEEE International Conference on Internet of Things, DSDIS/CPSCom/GreenCom/iThings 2015, Sydney, Australia, 11/12/15. https://doi.org/10.1109/DSDIS.2015.47

High-Performance FPGA Implementation of Modular Inversion over F₂₅₆ for Elliptic Curve Cryptography. / Hossain, Md Selim; Kong, Yinan.
Proceedings: 2015 IEEE international conference on data science and data intensive systems; the eighth IEEE international conference cyber, physical and social computing; the eleventh IEEE international conference on green computing and communications and the eighth IEEE international conference on internet of things. ed. / Jinjun Chen; Laurence T. Yang. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2015. p. 169-174.

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

TY - GEN

T1 - High-Performance FPGA Implementation of Modular Inversion over F256 for Elliptic Curve Cryptography

AU - Hossain, Md Selim

AU - Kong, Yinan

PY - 2015

Y1 - 2015

N2 - Modular Inversion over a prime field is an important operation for public-key cryptographic applications. It is the most crucial operation to speed up the calculation of an elliptic curve crypto-processor (ECC) when affine coordinates are used. In this work, the main goal is to implement a fast, high-performance modular inversion for ECC using field-programmable gate-array (FPGA) technology. A binary inversion algorithm in VHDL has been used for this efficient implementation. Timing simulation shows that the delay for one modular inversion operation in a modern Xilinx Virtex-7 FPGA is only 2.329 μs at the maximum frequency of 146.389 MHz. We have implemented an area-efficient design which takes a small amount of resources on the FPGA and needs only 1480 slices. To the best of the authors' knowledge, the proposed modular inversion over F256 provides a better performance than the available hardware implementations in terms of the area and the timing.

AB - Modular Inversion over a prime field is an important operation for public-key cryptographic applications. It is the most crucial operation to speed up the calculation of an elliptic curve crypto-processor (ECC) when affine coordinates are used. In this work, the main goal is to implement a fast, high-performance modular inversion for ECC using field-programmable gate-array (FPGA) technology. A binary inversion algorithm in VHDL has been used for this efficient implementation. Timing simulation shows that the delay for one modular inversion operation in a modern Xilinx Virtex-7 FPGA is only 2.329 μs at the maximum frequency of 146.389 MHz. We have implemented an area-efficient design which takes a small amount of resources on the FPGA and needs only 1480 slices. To the best of the authors' knowledge, the proposed modular inversion over F256 provides a better performance than the available hardware implementations in terms of the area and the timing.

KW - Elliptic curve cryptography (ECC)

KW - field-programmable gate-array (FPGA)

KW - modular inversion (MI)

KW - NIST (National Institute of Standards and Technology) prime field

KW - publickey cryptography (PKC)

UR - https://www.scopus.com/pages/publications/84964425133

U2 - 10.1109/DSDIS.2015.47

DO - 10.1109/DSDIS.2015.47

M3 - Conference proceeding contribution

AN - SCOPUS:84964425133

SP - 169

EP - 174

BT - Proceedings

A2 - Chen, Jinjun

A2 - Yang, Laurence T.

PB - Institute of Electrical and Electronics Engineers (IEEE)

CY - Piscataway, NJ

T2 - 2015 IEEE International Conference on Data Science and Data Intensive Systems; 8th IEEE International Conference Cyber, Physical and Social Computing; 11th IEEE International Conference on Green Computing and Communications and 8th IEEE International Conference on Internet of Things, DSDIS/CPSCom/GreenCom/iThings 2015

Y2 - 11 December 2015 through 13 December 2015

ER -

Hossain MS, Kong Y. High-Performance FPGA Implementation of Modular Inversion over F₂₅₆ for Elliptic Curve Cryptography. In Chen J, Yang LT, editors, Proceedings: 2015 IEEE international conference on data science and data intensive systems; the eighth IEEE international conference cyber, physical and social computing; the eleventh IEEE international conference on green computing and communications and the eighth IEEE international conference on internet of things. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE). 2015. p. 169-174 doi: 10.1109/DSDIS.2015.47