American Institute of Mathematical Sciences

Advanced
May  2010, 4(2): 169-187. doi: 10.3934/amc.2010.4.169

Efficient implementation of elliptic curve cryptography in wireless sensors

Diego F. Aranha 1, , Ricardo Dahab 1, , Julio López 1, and  Leonardo B. Oliveira 1,

1. 

University of Campinas (UNICAMP), Campinas - SP, CEP 13083-970, Brazil, Brazil, Brazil, Brazil

Received  June 2009 Revised  December 2009 Published  May 2010

The deployment of cryptography in sensor networks is a challenging task, given the limited computational power and the resource-constrained nature of the sensoring devices. This paper presents the implementation of elliptic curve cryptography in the MICAz Mote, a popular sensor platform. We present optimization techniques for arithmetic in binary fields, including squaring, multiplication and modular reduction at two different security levels. Our implementation of field multiplication and modular reduction algorithms focuses on the reduction of memory accesses and appears as the fastest result for this platform. Finite field arithmetic was implemented in C and Assembly and elliptic curve arithmetic was implemented in Koblitz and generic binary curves. We illustrate the performance of our implementation with timings for key agreement and digital signature protocols. In particular, a key agreement can be computed in 0.40 seconds and a digital signature can be computed and verified in 1 second at the 163-bit security level. Our results strongly indicate that binary curves are the most efficient alternative for the implementation of elliptic curve cryptography in this platform.
Keywords: elliptic curve cryptography, finite field arithmetic., Efficient software implementation, cryptographic engineering.
Mathematics Subject Classification: Primary: 11-04; Secondary: 94A6.
Citation: Diego F. Aranha, Ricardo Dahab, Julio López, Leonardo B. Oliveira. Efficient implementation of elliptic curve cryptography in wireless sensors. Advances in Mathematics of Communications, 2010, 4 (2) : 169-187. doi: 10.3934/amc.2010.4.169
[1]

Gerhard Frey. Relations between arithmetic geometry and public key cryptography. Advances in Mathematics of Communications, 2010, 4 (2) : 281-305. doi: 10.3934/amc.2010.4.281
[2]

Haibo Yi. Efficient systolic multiplications in composite fields for cryptographic systems. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1135-1145. doi: 10.3934/dcdss.2019078
[3]

Florian Luca, Igor E. Shparlinski. On finite fields for pairing based cryptography. Advances in Mathematics of Communications, 2007, 1 (3) : 281-286. doi: 10.3934/amc.2007.1.281
[4]

Huaiyu Jian, Hongjie Ju, Wei Sun. Traveling fronts of curve flow with external force field. Communications on Pure & Applied Analysis, 2010, 9 (4) : 975-986. doi: 10.3934/cpaa.2010.9.975
[5]

Koray Karabina, Berkant Ustaoglu. Invalid-curve attacks on (hyper)elliptic curve cryptosystems. Advances in Mathematics of Communications, 2010, 4 (3) : 307-321. doi: 10.3934/amc.2010.4.307
[6]

Anton Stolbunov. Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Advances in Mathematics of Communications, 2010, 4 (2) : 215-235. doi: 10.3934/amc.2010.4.215
[7]

Steven D. Galbraith, Ping Wang, Fangguo Zhang. Computing elliptic curve discrete logarithms with improved baby-step giant-step algorithm. Advances in Mathematics of Communications, 2017, 11 (3) : 453-469. doi: 10.3934/amc.2017038
[8]

Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237-244. doi: 10.3934/amc.2017015
[9]

Andrew P. Sage. Risk in system of systems engineering and management. Journal of Industrial & Management Optimization, 2008, 4 (3) : 477-487. doi: 10.3934/jimo.2008.4.477
[10]

M. J. Jacobson, R. Scheidler, A. Stein. Cryptographic protocols on real hyperelliptic curves. Advances in Mathematics of Communications, 2007, 1 (2) : 197-221. doi: 10.3934/amc.2007.1.197
[11]

Akbar Mahmoodi Rishakani, Seyed Mojtaba Dehnavi, Mohmmadreza Mirzaee Shamsabad, Nasour Bagheri. Cryptographic properties of cyclic binary matrices. Advances in Mathematics of Communications, 2019, 0 (0) : 0-0. doi: 10.3934/amc.2020068
[12]

Tanja Eisner, Rainer Nagel. Arithmetic progressions -- an operator theoretic view. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 657-667. doi: 10.3934/dcdss.2013.6.657
[13]

Mehdi Pourbarat. On the arithmetic difference of middle Cantor sets. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4259-4278. doi: 10.3934/dcds.2018186
[14]

Eitan Altman. Bio-inspired paradigms in network engineering games. Journal of Dynamics & Games, 2014, 1 (1) : 1-15. doi: 10.3934/jdg.2014.1.1
[15]

Andreas Klein. How to say yes, no and maybe with visual cryptography. Advances in Mathematics of Communications, 2008, 2 (3) : 249-259. doi: 10.3934/amc.2008.2.249
[16]

Qichun Wang, Chik How Tan, Pantelimon Stănică. Concatenations of the hidden weighted bit function and their cryptographic properties. Advances in Mathematics of Communications, 2014, 8 (2) : 153-165. doi: 10.3934/amc.2014.8.153
[17]

Gérard Maze, Chris Monico, Joachim Rosenthal. Public key cryptography based on semigroup actions. Advances in Mathematics of Communications, 2007, 1 (4) : 489-507. doi: 10.3934/amc.2007.1.489
[18]

Ruinian Li, Yinhao Xiao, Cheng Zhang, Tianyi Song, Chunqiang Hu. Cryptographic algorithms for privacy-preserving online applications. Mathematical Foundations of Computing, 2018, 1 (4) : 311-330. doi: 10.3934/mfc.2018015
[19]

Pascale Charpin, Jie Peng. Differential uniformity and the associated codes of cryptographic functions. Advances in Mathematics of Communications, 2019, 13 (4) : 579-600. doi: 10.3934/amc.2019036
[20]

Jintai Ding, Sihem Mesnager, Lih-Chung Wang. Letters for post-quantum cryptography standard evaluation. Advances in Mathematics of Communications, 2020, 14 (1) : i-i. doi: 10.3934/amc.2020012

2018 Impact Factor: 0.879

Tools

Metrics

  • PDF downloads (64)
  • HTML views (0)
  • Cited by (17)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences