Paper Info
Title
Exploring the design space of prime field vs. binary field ECC-Hardware implementations
Abstract
In this paper, we answer the question whether binary extension field or prime-field based processors doing multi-precision arithmetic are better in the terms of area, speed, power, and energy. This is done by implementing and optimizing two distinct custom-made 16-bit processor designs and comparing our solutions on different abstraction levels: finite-field arithmetic, elliptic-curve operations, and on protocol level by implementing the Elliptic Curve Digital Signature Algorithm (ECDSA). On the one hand, our $\mathbb{F}_{2^{m}}$ based processor outperforms the $\mathbb{F}_p$ based processor by 19.7% in area, 69.6% in runtime, 15.9% in power, and 74.4% in energy when performing a point multiplication. On the other hand, our $\mathbb{F}_p$ based processor (11.6kGE, 41.4,μ W, 1,313kCycles, and 54.3μ J) improves the state-of-the-art in $\mathbb{F}_{p_{192}}$ ECC hardware implementations regarding area, power, and energy results. After extending the designs for ECDSA (signature generation and verification), the area and power-consumption advantages of the $\mathbb{F}_{2^{m}}$ based processor vanish, but it still is 1.5-2.8 times better in terms of energy and runtime.
Year
DOI
Venue
2011
10.1007/978-3-642-29615-4_18
NordSec
Keywords
Field
DocType
elliptic-curve operation,binary extension field,design space,multi-precision arithmetic,ecc-hardware implementation,prime field,point multiplication,different abstraction level,energy result,binary field,elliptic curve digital signature,finite-field arithmetic,ecc hardware,distinct custom-made 16-bit processor
Design space,Elliptic Curve Digital Signature Algorithm,Discrete mathematics,Hardware implementations,Prime field,Computer science,Binary fields,Algorithm,Multiplication,Elliptic curve cryptography,Binary number
Conference
Volume
ISSN
Citations 
7161
0302-9743
7
PageRank 
References 
Authors
0.46
18
2
Name
Order
Citations
PageRank
Erich Wenger117511.16
Michael Hutter234525.26