## TinyECC: A Configurable Library for
Elliptic Curve Cryptography
in Wireless Sensor Networks
(Version 1.0)
*Released on 11/2/07.*
### Introduction
TinyECC 1.0 is a software package providing ECC-based PKC
operations that can be flexibly configured and integrated into
sensor network applications. It provides a digital signature
scheme (ECDSA), a key exchange protocol (ECDH), and a public
key encryption scheme (ECIES). TinyECC uses a number of
optimization switches, which can turn specific optimizations on or
off based on developer's needs.
TinyECC 1.0 is intended for sensor platforms running TinyOS. The current version is implemented in nesC, with additional platform-specific optimizations in inline assembly for popular sensor platforms. It has been tested on MICAz, TelosB, Tmote Sky,
and Imote2. TinyECC 1.0 supports SECG recommended 128-bit, 160-bit and 192-bit elliptic curve domain parameters.
For questions please contact An Liu at *aliu3 (at) ncsu.edu*.
### What's new in version 1.0
- Support for ECIES and ECDH
- Point compress and uncompress form of ECIES
- Point compress form enabled by default
- Configurability
- All optimizations can be turned on or off at compile time with switches
- Support of more optimization techniques
(for faster execution or more compact code size)
- Barrett reduction
- Mixed Jacobian-affine points addition
- Repeated point doubling
- Affine coordinate point addition and doubling
- Support for hybrid multiplication and squaring (inline assembly) for TelosB/Tmote Sky and Imote2
### People
### Platform
- MICAz, TelosB/Tmote Sky, and Imote2 running
TinyOS
### Related Software
### Related Documents
### Download
### How to Use
- Please check README for details.
- If you need to cite the TinyECC paper, please use the following:
An Liu, Peng Ning, "TinyECC: A Configurable Library for Elliptic Curve Cryptography in Wireless Sensor Networks," in *Proceedings of the 7th International Conference on Information Processing in Sensor Networks (IPSN 2008)*, SPOTS Track, pages 245--256, April 2008.
- If you need to cite the TinyECC distribution site, please use the following:
An Liu,
Peng Ning, "TinyECC: Elliptic Curve Cryptography for Sensor Networks (Version
1.0)", http://discovery.csc.ncsu.edu/software/TinyECC/,
November 2007.
### Performance Results
The following performance results were measured on MICAz,
TelosB/Tmote Sky, and Imote2 running TinyOS using *secp160r1*,
which is elliptic
curve domain parameter over F_{p}[7]
recommended by Standards for Efficient Cryptography Group (SECG).
We enable all optimization switches and disable all optimization
switches to show the most computation-efficient case and most
storage-efficient case.
**Most computation efficient case**
First, we enable all optimization switches to
show how fast TinyECC could be.
**Figure 1: Execution time (ms) when all
optimization switches enabled**
As figure 1 shows, TelosB(4 MHz) is the slowest
platform, Imote2(416 MHz) is the fastest platform. TelosB(4 MHz)
needs 3,169 ms for signature generation, and 4040 ms for signature
verification. Imote2(416 MHz) only needs 12 ms for signature
generation, and 14 ms for signature verification. Figure 2 shows
the code size in most computation efficient case. Imote2 requires
largest RAM usage due to its 32-bit word size. MICAz has the
largest ROM usage due to its additional inline assembly code for
curve specific optimization.
**Figure 2: Code size (byte) when all
optimization switches enabled**
We used the formula E = U*I*t to estimate the energy consumption of signature generation and verification. For MICAz, when processor is in active mode, I = 8
mA. For TelosB, I = 1.8mA for active mode. Typically, U = 3.0 V if two new AA batteries are used.
When Imote2 runs at 13 MHz, the core voltage is set to 850mV and
current draw is 31mA with radio off. When it runs at 104 MHz, the
core voltage is set to 950mV and current draw is 66mA with radio
on. All these data are from datasheets of crossbow product[12].
**Figure 3: Energy consumption (mJ) when all
optimization switches enabled**
As figure 3 shows, MICAz is the most energy consuming
platform, Imote2 is energy efficient even when it runs at 104 MHz with
radio on.
Due to the resource constraint of low end sensor
platforms (e.g. MICAz, TelosB/Tmote Sky), sometimes we need to reduce the
code size (by disabling some optimization switches) to integrate TinyECC
with other TinyOS applications. Next, we disable all the optimization
switches to show how compact TinyECC could be.
**Figure 4: Execution time (ms) when all optimization
switches disabled**
When all optimization switches are disabled, although all
ECDSA, ECIES, and ECDH operations are slowed down, the code size is reduced
dramatically as figure 5 shows. For example, the RAM requirement is only
around 150 bytes for MICAz. The ROM size of ECIES for MICAz is reduced from
20,768 bytes to 12,442 bytes.
**Figure 5: Code size (byte) when all optimization
switches disabled**
**Figure 6: Energy consumption (mJ) when all optimization
switches disabled**
Since the execution time is increased lot, the energy
consumption of all platforms are increased too. MICAz even needs 15 and 25
times more energy for ECDSA signature generation and verification compared
with most computation efficient case.
### Techniques Adopted in TinyECC
We have implemented several well known optimizations for TinyECC.
We provide several switches to enable and disable each of them
according to developer's needs. However, this implementation does not
include all known optimizations, such as Non-Adjacent Forms.
Barrett reduction is an alternative method for modular reduction [9].
It converts the reduction modulo an arbitrary integer to two
multiplications and a few reductions modulo integers of the form 2^{n}.
When used to reduce various numbers modulo a single number many
times, Barrett reduction can be faster than modular reductions
obtained by division.
There is no division instruction for ATmega128, so the inverse
operation is significantly more expensive than multiplication. It is
efficient to implement elliptic curve operations in projective
coordinates instead of affine coordinates. We used *weighted
projective* representation (*Jacobian* representation) [1]
in TinyECC to speed up point addition, point doubling and scalar
point multiplication.
For all NIST and most SECG curves, the underlying field primes * p*
were chosen as pseudo-Mersenne primes to allow optimized modular
reduction [2]. We implemented this optimized
modular reduction algorithm to speed up modular multiplication and modular square.
We implemented the sliding window method to speed up scalar point
multiplication. The traditional method to do scalar point
multiplication is binary method. Binary method scans bits of scalar
n from left to right, one bit at a time. A point doubling is performed at each step.
Depending on the scanned bit value, a subsequent point addition is
performed. Sliding window method [3] scans * k* bits at
a time. Point doubling is performed * k* times at each step, depending
on the scanned * k* bits value a subsequent point addition is
performed. We have to pre-compute all the added points, which is the
result of possible * k* bits value multiply the base point. The
sliding window method can speed up scalar point multiplication by reducing the
total number of point additions, but extra memory is required.
The natural number operations in TinyECC are based on the implementation in RSAREF2.0 [6]. The natural number operations in RSAREF 2.0 are platform
independent, but they are not efficient. We used inline assembly
code [4][10][11] to speed up critical operations such as multiplication and squaring for MICAz,
TelosB/Tmote Sky, and Imote2 motes. In particular, hybrid multiplication in [2] is implemented in inline assembly, which can speed up TinyECC effectively..
We implemented algorithms 2.7 and 2.8 in [5]
to speed up modular addition and modular subtraction.
We applied algorithm 3.48 in [5] to reduce
the signature verification time.
### Copyright and Disclaimer
All new code in this distribution is Copyright
2007 by North
Carolina State University. All rights reserved. Redistribution and use
in source and binary forms are permitted provided that this entire
copyright notice is duplicated in all such copies, and that any
documentation, announcements, and other materials related to such
distribution and use acknowledge that the software was developed at
North Carolina State University, Raleigh, NC. No charge may be made
for copies, derivations, or distributions of this material without the
express written consent of the copyright holder. Neither the name of
the University nor the name of the author may be used to endorse or
promote products derived from this material without specific prior
written permission.
IN NO EVENT SHALL THE NORTH CAROLINA STATE UNIVERSITY BE LIABLE TO
ANY PARTY FOR DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL
DAMAGES ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION,
EVEN IF THE NORTH CAROLINA STATE UNIVERSITY HAS BEEN ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE. THE SOFTWARE PROVIDED HEREUNDER IS ON AN "AS IS" BASIS, AND THE NORTH CAROLINA STATE UNIVERSITY HAS
NO OBLIGATION TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS,
OR MODIFICATIONS."
### Acknowledgment
The natural number operations in TinyECC are based on the implementation in RSAREF 2.0 [6].
### References
[1] I. Blake, G. Seroussi, and N. Smart. Elliptic
Curves in Cryptography. Cambridge University Press, 1999. London
Mathematical Society Lecture Note Series 265.
[2] N. Gura, A. Patel, and A. Wander. Comparing
elliptic curve cryptography and RSA on 8-bit CPUs. In *Proceedings
of the 2004 Workshop on Cryptographic Hardware and Embedded Systems
(CHES 2004)*, August 2004.
[3] Çetin Kaya Kac. High-Speed RSA
Implementation, RSA Laboratories Technical Report TR-201, Version
2.0, November 22, 1994.
[4] 8-bit AVR Instruction Set. http://www.atmel.com/dyn/resources/prod_documents/DOC0856.PDF
[5] D. Hankerson, A. Menezens, and S. Vanstone.
*Guide to Elliptic Curve Cryptography*. Springer, 2004.
[6] RSA Laboratories. RSAREF: A cryptographic
toolkit (version 2.0), March 1994.
[7] Certicom Research. Standards for efficient
cryptography - SEC2: Recommended elliptic curve domain parameters. http://www.secg.org/download/aid-386/sec2_final.pdf,
September 2000.
[8] D. Eastlake, P. Jones. US Secure Hash Algorithm 1 (SHA1). RFC
3174, September 2001.
[9] A. Menezes, P. Oorschot,
and S. Vanstone, "Handbook
of Applied Cryptography," CRC Press, 1997.
[10] MSP430x1xx Family User's
Guide (Rev. F), http://focus.ti.com/lit/ug/slau049f/slau049f.pdf.
[11] ARM v5TE
Architecture Reference Manual, http://www.arm.com/documentation/Instruction_Set/index.html.
[12] Crossbow, http://www.xbow.com.
### Sponsors
This project has been generously supported by
*This material is based upon work supported by the National Science Foundation (NSF) under grant CAREER-0447761 and US Army Research Office (ARO) under grant W911NF-05-1-0247. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or the ARO.* |