Design and Implementation of High-Performance ECC Processor with Unified Point Addition on Twisted Edwards Curve

Md Mainul Islam,Yeong Min Jang,Md Selim Hossain,Moh Khalid Hasan,Md Shahjalal

doi:10.3390/s20185148

Abstract

With the swift evolution of wireless technologies, the demand for the Internet of Things (IoT) security is rising immensely. Elliptic curve cryptography (ECC) provides an attractive solution to fulfill this demand. In recent years, Edwards curves have gained widespread acceptance in digital signatures and ECC due to their faster group operations and higher resistance against side-channel attacks (SCAs) than that of the Weierstrass form of elliptic curves. In this paper, we propose a high-speed, low-area, simple power analysis (SPA)-resistant field-programmable gate array (FPGA) implementation of ECC processor with unified point addition on a twisted Edwards curve, namely Edwards25519. Efficient hardware architectures for modular multiplication, modular inversion, unified point addition, and elliptic curve point multiplication (ECPM) are proposed. To reduce the computational complexity of ECPM, the ECPM scheme is designed in projective coordinates instead of affine coordinates. The proposed ECC processor performs 256-bit point multiplication over a prime field in 198,715 clock cycles and takes 1.9 ms with a throughput of 134.5 kbps, occupying only 6543 slices on Xilinx Virtex-7 FPGA platform. It supports high-speed public-key generation using fewer hardware resources without compromising the security level, which is a challenging requirement for IoT security.

Highlights

The Internet of Things (IoT) refers a global network, where billions of devices are connected through the Internet and share data with each other
The proposed Elliptic curve cryptography (ECC) processor was programmed in VHDL and implemented using the Xilinx
Conventional DAA method is adopted for elliptic curve point multiplication (ECPM), where point addition (PA) and point doubling (PD) are executed by separate modules carrying high risk of simple power analysis (SPA) attacks

Summary

Introduction

The Internet of Things (IoT) refers a global network, where billions of devices are connected through the Internet and share data with each other. Since most of these devices have constrained resources, data are usually stored in the cloud, where people can continuously upload and download data from anywhere via the Internet [1]. The importance of data security and the limited resources of IoT devices motivate us to install lightweight cryptographic schemes that can satisfy the security, low-energy, and low-memory requirements of the existing IoT applications. ECC can be implemented with low hardware resource usage and low energy consumption without degrading its security

Methods

Results

Conclusion