author        = {Erich Wenger and Michael Hutter},
  title         = {Exploring the Design Space of Prime Field vs. Binary Field ECC-Hardware Implementations},
  booktitle     = {Nordic Conference on Secure IT Systems -- NordSec 2011, 16th Edition, Tallinn, Estonia, October 26-28},
  year          = {2011},
  editor        = {Peeter Laud},
  volume        = {7161},
  series        = {Lecture Notes in Computer Science},
  pages         = {256--271},
  publisher     = {Springer Berlin Heidelberg},
  doi           = {10.1007/978-3-642-29615-4_18},
  keywords      = {Hardware Implementation, Elliptic Curve Cryptography, ECC, ECDSA, Binary-Extension Field, Prime Field},
  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,uW, 1,313kCycles, and 54.3uJ) 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.},