Reconfigurable Hardware Architecture for Authenticated Key Agreement Protocol Over Binary Edwards Curve

Nalla Anandakumar, Mohammad Hashmi

Research output: Contribution to journalArticle

Abstract

In this article, we present a high-performance hardware architecture for Elliptic curve based (authenticated) key agreement protocol “Elliptic Curve Menezes, Qu and Vanstone” (ECMQV) over Binary Edwards Curve (BEC). We begin by analyzing inversion module on a 251-bit binary field. Subsequently, we present Field Programmable Gate Array (FPGA) implementations of the unified formula for computing elliptic curve point addition on BEC in affine and projective coordinates and investigate the relative performance of these two coordinates. Then, we implement the w-coordinate based differential addition formulae suitable for usage in Montgomery ladder. Next, we present a novel hardware architecture of BEC point multiplication using mixed w-coordinates of the Montgomery laddering algorithm and analyze it in terms of resistance to Simple Power Analysis (SPA) attack. In order to improve the performance, the architecture utilizes registers efficiently and uses efficient scheduling mechanisms for the BEC arithmetic implementations. Our implementation results show that the proposed architecture is resistant against SPA attack and yields a better performance when compared to the existing state-of-the-art BEC designs for computing point multiplication (PM). Finally, we present an FPGA design of ECMQV key agreement protocol using BEC defined over GF(2251). The execution of ECMQV protocol takes 66.47μs using 32,479 slices on Virtex-4 FPGA and 52.34μs using 15,988 slices on Virtex-5 FPGA. To the best of our knowledge, this is the first FPGA design of the ECMQV protocol using BEC.
Original languageEnglish
Pages (from-to)12:1-12:19
Number of pages19
JournalACM Transactions on Reconfigurable Technology and Systems
Volume11
Issue number2
Publication statusPublished - Nov 30 2018

Fingerprint

Reconfigurable hardware
Field programmable gate arrays (FPGA)
Hardware
Ladders
Scheduling

Cite this

Reconfigurable Hardware Architecture for Authenticated Key Agreement Protocol Over Binary Edwards Curve. / Anandakumar, Nalla; Hashmi, Mohammad.

In: ACM Transactions on Reconfigurable Technology and Systems, Vol. 11, No. 2, 30.11.2018, p. 12:1-12:19.

Research output: Contribution to journalArticle

@article{260a1389ea05497faec8ae35bbc8bc66,
title = "Reconfigurable Hardware Architecture for Authenticated Key Agreement Protocol Over Binary Edwards Curve",
abstract = "In this article, we present a high-performance hardware architecture for Elliptic curve based (authenticated) key agreement protocol “Elliptic Curve Menezes, Qu and Vanstone” (ECMQV) over Binary Edwards Curve (BEC). We begin by analyzing inversion module on a 251-bit binary field. Subsequently, we present Field Programmable Gate Array (FPGA) implementations of the unified formula for computing elliptic curve point addition on BEC in affine and projective coordinates and investigate the relative performance of these two coordinates. Then, we implement the w-coordinate based differential addition formulae suitable for usage in Montgomery ladder. Next, we present a novel hardware architecture of BEC point multiplication using mixed w-coordinates of the Montgomery laddering algorithm and analyze it in terms of resistance to Simple Power Analysis (SPA) attack. In order to improve the performance, the architecture utilizes registers efficiently and uses efficient scheduling mechanisms for the BEC arithmetic implementations. Our implementation results show that the proposed architecture is resistant against SPA attack and yields a better performance when compared to the existing state-of-the-art BEC designs for computing point multiplication (PM). Finally, we present an FPGA design of ECMQV key agreement protocol using BEC defined over GF(2251). The execution of ECMQV protocol takes 66.47μs using 32,479 slices on Virtex-4 FPGA and 52.34μs using 15,988 slices on Virtex-5 FPGA. To the best of our knowledge, this is the first FPGA design of the ECMQV protocol using BEC.",
author = "Nalla Anandakumar and Mohammad Hashmi",
year = "2018",
month = "11",
day = "30",
language = "English",
volume = "11",
pages = "12:1--12:19",
journal = "ACM Transactions on Reconfigurable Technology and Systems",
issn = "1936-7406",
publisher = "Association for Computing Machinery (ACM)",
number = "2",

}

TY - JOUR

T1 - Reconfigurable Hardware Architecture for Authenticated Key Agreement Protocol Over Binary Edwards Curve

AU - Anandakumar, Nalla

AU - Hashmi, Mohammad

PY - 2018/11/30

Y1 - 2018/11/30

N2 - In this article, we present a high-performance hardware architecture for Elliptic curve based (authenticated) key agreement protocol “Elliptic Curve Menezes, Qu and Vanstone” (ECMQV) over Binary Edwards Curve (BEC). We begin by analyzing inversion module on a 251-bit binary field. Subsequently, we present Field Programmable Gate Array (FPGA) implementations of the unified formula for computing elliptic curve point addition on BEC in affine and projective coordinates and investigate the relative performance of these two coordinates. Then, we implement the w-coordinate based differential addition formulae suitable for usage in Montgomery ladder. Next, we present a novel hardware architecture of BEC point multiplication using mixed w-coordinates of the Montgomery laddering algorithm and analyze it in terms of resistance to Simple Power Analysis (SPA) attack. In order to improve the performance, the architecture utilizes registers efficiently and uses efficient scheduling mechanisms for the BEC arithmetic implementations. Our implementation results show that the proposed architecture is resistant against SPA attack and yields a better performance when compared to the existing state-of-the-art BEC designs for computing point multiplication (PM). Finally, we present an FPGA design of ECMQV key agreement protocol using BEC defined over GF(2251). The execution of ECMQV protocol takes 66.47μs using 32,479 slices on Virtex-4 FPGA and 52.34μs using 15,988 slices on Virtex-5 FPGA. To the best of our knowledge, this is the first FPGA design of the ECMQV protocol using BEC.

AB - In this article, we present a high-performance hardware architecture for Elliptic curve based (authenticated) key agreement protocol “Elliptic Curve Menezes, Qu and Vanstone” (ECMQV) over Binary Edwards Curve (BEC). We begin by analyzing inversion module on a 251-bit binary field. Subsequently, we present Field Programmable Gate Array (FPGA) implementations of the unified formula for computing elliptic curve point addition on BEC in affine and projective coordinates and investigate the relative performance of these two coordinates. Then, we implement the w-coordinate based differential addition formulae suitable for usage in Montgomery ladder. Next, we present a novel hardware architecture of BEC point multiplication using mixed w-coordinates of the Montgomery laddering algorithm and analyze it in terms of resistance to Simple Power Analysis (SPA) attack. In order to improve the performance, the architecture utilizes registers efficiently and uses efficient scheduling mechanisms for the BEC arithmetic implementations. Our implementation results show that the proposed architecture is resistant against SPA attack and yields a better performance when compared to the existing state-of-the-art BEC designs for computing point multiplication (PM). Finally, we present an FPGA design of ECMQV key agreement protocol using BEC defined over GF(2251). The execution of ECMQV protocol takes 66.47μs using 32,479 slices on Virtex-4 FPGA and 52.34μs using 15,988 slices on Virtex-5 FPGA. To the best of our knowledge, this is the first FPGA design of the ECMQV protocol using BEC.

M3 - Article

VL - 11

SP - 12:1-12:19

JO - ACM Transactions on Reconfigurable Technology and Systems

JF - ACM Transactions on Reconfigurable Technology and Systems

SN - 1936-7406

IS - 2

ER -