Reconfigurable Architecture for Elliptic Curve Cryptography Using FPGA

A Kaleel Rahuman,G Athisha

doi:10.1155/2013/675161

Abstract

The high performance of an elliptic curve (EC) crypto system depends efficiently on the arithmetic in the underlying finite field. We have to propose and compare three levels of Galois Field <svg style="vertical-align:-2.3205pt;width:58.950001px;" id="M1" height="18.799999" version="1.1" viewBox="0 0 58.950001 18.799999" width="58.950001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,15.85)"><path id="x47" d="M692 302v-28q-45 -6 -54.5 -17t-9.5 -55v-86q0 -62 7 -95q-7 -2 -32 -7.5l-37 -8l-35.5 -7.5t-40.5 -7t-38.5 -4t-40.5 -2q-165 0 -266 93t-101 243q0 84 32 151t86 108t121.5 63t142.5 22q29 0 62.5 -4t52 -7.5t47.5 -10.5t31 -7l15 -156l-28 -6q-17 87 -66.5 121.5
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l-26 -65h-233z" /></g><g transform="matrix(.012,-0,0,-.012,46.673,7.688)"><use xlink:href="#x36"/></g> <g transform="matrix(.017,-0,0,-.017,53.012,15.85)"><use xlink:href="#x29"/></g> </svg>. The proposed architecture is based on Lopez-Dahab elliptic curve point multiplication algorithm, which uses Gaussian normal basis for <svg style="vertical-align:-2.3205pt;width:58.950001px;" id="M4" height="18.799999" version="1.1" viewBox="0 0 58.950001 18.799999" width="58.950001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,15.85)"><use xlink:href="#x47"/></g><g transform="matrix(.017,-0,0,-.017,12.217,15.85)"><use xlink:href="#x46"/></g><g transform="matrix(.017,-0,0,-.017,21.209,15.85)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,27.091,15.85)"><use xlink:href="#x32"/></g> <g transform="matrix(.012,-0,0,-.012,35.25,7.688)"><use xlink:href="#x31"/></g><g transform="matrix(.012,-0,0,-.012,40.961,7.688)"><use xlink:href="#x36"/></g><g transform="matrix(.012,-0,0,-.012,46.673,7.688)"><use xlink:href="#x33"/></g> <g transform="matrix(.017,-0,0,-.017,53.012,15.85)"><use xlink:href="#x29"/></g> </svg> field arithmetic. The proposed <svg style="vertical-align:-2.3205pt;width:58.950001px;" id="M5" height="18.725" version="1.1" viewBox="0 0 58.950001 18.725" width="58.950001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x47"/></g><g transform="matrix(.017,-0,0,-.017,12.217,15.775)"><use xlink:href="#x46"/></g><g transform="matrix(.017,-0,0,-.017,21.209,15.775)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,27.091,15.775)"><use xlink:href="#x32"/></g> <g transform="matrix(.012,-0,0,-.012,35.25,7.613)"><use xlink:href="#x31"/></g><g transform="matrix(.012,-0,0,-.012,40.961,7.613)"><use xlink:href="#x39"/></g><g transform="matrix(.012,-0,0,-.012,46.673,7.613)"><use xlink:href="#x33"/></g> <g transform="matrix(.017,-0,0,-.017,53.012,15.775)"><use xlink:href="#x29"/></g> </svg> is based on an efficient Montgomery add and double algorithm, also the Karatsuba-Ofman multiplier and Itoh-Tsujii algorithm are used as the inverse component. The hardware design is based on optimized finite state machine (FSM), with a single cycle 193 bits multiplier, field adder, and field squarer. The another proposed architecture <svg style="vertical-align:-2.3205pt;width:58.950001px;" id="M6" height="18.799999" version="1.1" viewBox="0 0 58.950001 18.799999" width="58.950001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,15.85)"><use xlink:href="#x47"/></g><g transform="matrix(.017,-0,0,-.017,12.217,15.85)"><use xlink:href="#x46"/></g><g transform="matrix(.017,-0,0,-.017,21.209,15.85)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,27.091,15.85)"><use xlink:href="#x32"/></g> <g transform="matrix(.012,-0,0,-.012,35.25,7.688)"><use xlink:href="#x32"/></g><g transform="matrix(.012,-0,0,-.012,40.961,7.688)"><use xlink:href="#x35"/></g><g transform="matrix(.012,-0,0,-.012,46.673,7.688)"><use xlink:href="#x36"/></g> <g transform="matrix(.017,-0,0,-.017,53.012,15.85)"><use xlink:href="#x29"/></g> </svg> is based on applications for which compactness is more important than speed. The FPGA’s dedicated multipliers and carry-chain logic are used to obtain the small data path. The different optimization at the hardware level improves the acceleration of the ECC scalar multiplication, increases frequency and the speed of operation such as key generation, encryption, and decryption. Finally, we have to implement our design using Xilinx XC4VLX200 FPGA device.

Highlights

Many hardware designs of elliptic curve cryptography have been developed, aiming to accelerate the scalar multiplication processes, mainly those based on the field programmable gate arrays (FPGAs)
The main contribution of the present research concerned three major points: an optimal finite state machine (FSM) controlling the whole components, minimizing empty cycles; optimization of the inversion process, by reducing the number of different squaring from 192 to 21, leading to an inversion; separation of the data path routing from the control part, in order to modify only the multiplier, the squarer, the adder and the modulo components
We have presented the design of a fast version of elliptic curve (EC) cryptohardware based on a Finite State Machine

Summary

Introduction

Many hardware designs of elliptic curve cryptography have been developed, aiming to accelerate the scalar multiplication processes, mainly those based on the field programmable gate arrays (FPGAs). More and more FPGA implementations are in an environment which used to be ASIC-only territory. When these applications are implemented on an FPGA, they need secure data communication. In this rapidly changing environment, the reconfigurability of an FPGA is a very useful feature which is not available on an ASIC. It is the ability to embed a strategic and strong algorithm in very few hardware, that is, finding an optimal solution to the one to many problem: portability against power consumption, speed against area, but the main issue in cryptography is security

Methods

Results

Conclusion