Cyber Defense Laboratory

 

 

TinyECC: A Configurable Library for Elliptic Curve Cryptography
in Wireless Sensor Networks
(Version 2.0)

Released on 2/3/2011.

Introduction

TinyECC 2.0 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 2.0 is intended for sensor platforms running TinyOS-2.x. The current version is implemented in nesC, with additional platform-specific optimizations in inline assembly for popular sensor platforms. It has been tested on MICA2/MICAz, TelosB/Tmote Sky, BSNV3, and Imote2. TinyECC 2.0 supports SECG recommended 128-bit, 160-bit and 192-bit elliptic curve domain parameters.

For questions please contact Peng Ning at pning (at) ncsu.edu.

What's new in version 2.0

  • Support for TinyOS-2.x

People

Platform

  • MICAz, TelosB/Tmote Sky, and Imote2 running TinyOS-2.x

Related Software

Related Documents

Download

  • Click here to 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 2.0)", http://discovery.csc.ncsu.edu/software/TinyECC/, August 2010.

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 (BARRETT)

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 2n. When used to reduce various numbers modulo a single number many times, Barrett reduction can be faster than modular reductions obtained by division.

  • Projective Coordinate Systems (PROJECTIVE)

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.

  • Curve-Specific Optimizations (CURVE_OPT)

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.

  • Sliding Window Method (SLIDING_WIN

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.

  • Inline Assembly and Hybrid Multiplication (HYBRID_MULT, HYBRID_SQR)

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..

  • Optimization for Modular Addition and Modular Subtraction

We implemented algorithms 2.7 and 2.8 in [5] to speed up modular addition and modular subtraction.

  • Shamir's Trick (SHAMIR_TRICK)

We applied algorithm 3.48 in [5] to reduce the signature verification time.

Copyright and Disclaimer

All new code in this distribution is Copyright 2010 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

NSF
ARO
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.
 
 
©2010 Peng Ning. Last Updated February 3, 2011 .