### Twisted Edwards-Form Elliptic Curve Cryptography for 8-bit AVR-based Sensor Nodes

Dalin Chu, Johann Großschädl, Zhe Liu, Volker Müller, and Yang Zhang

##### Abstract

Wireless Sensor Networks (WSNs) pose a number of unique security challenges that demand innovation in several areas including the design of cryptographic primitives and protocols. Despite recent progress, the efficient implementation of Elliptic Curve Cryptography (ECC) for WSNs is still a very active research topic and techniques to further reduce the time and energy cost of ECC are eagerly sought. This paper presents an optimized ECC implementation that we developed from scratch to comply with the severe resource constraints of 8-bit sensor nodes such as the MICAz and IRIS motes. Our ECC software uses Optimal Prime Fields (OPFs) as underlying algebraic structure and supports two different families of elliptic curves, namely Weierstraß-form and twisted Edwards-form curves. Due to the combination of efficient field arithmetic and fast group operations, we achieve an execution time of $5.8 \cdot 10^6$ clock cycles for a full 158-bit scalar multiplication on an 8-bit ATmega128 microcontroller, which is 2.78 times faster than the widely-used TinyECC library. Our implementation also shows that the energy cost of scalar multiplication on a MICAz (or IRIS) mote amounts to just 19 mJ when using a twisted Edwards curve over a 160-bit OPF. This result compares fairly well with the energy figures of two recently-presented hardware designs of ECC based on twisted Edwards curves.

Available format(s)
Category
Implementation
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curve cryptosystem
Contact author(s)
johann groszschaedl @ uni lu
History
2013-03-26: last of 2 revisions
See all versions
Short URL
https://ia.cr/2012/730

CC BY

BibTeX

@misc{cryptoeprint:2012/730,
author = {Dalin Chu and Johann Großschädl and Zhe Liu and Volker Müller and Yang Zhang},
title = {Twisted Edwards-Form Elliptic Curve Cryptography for 8-bit AVR-based Sensor Nodes},
howpublished = {Cryptology ePrint Archive, Paper 2012/730},
year = {2012},
note = {\url{https://eprint.iacr.org/2012/730}},
url = {https://eprint.iacr.org/2012/730}
}

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