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Efficient software implementation of public-key cryptography on sensor networks using the MSP430X microcontroller

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Abstract

In this work, we describe a software implementation of elliptic curve cryptography and pairing-based cryptography for the MSP430 microcontroller family, which is used in wireless sensors. Digital signature, short signature and key distribution protocols were implemented at the 80- and 128-bit levels of security, over both binary and prime fields. The timing results of our software implementation show an improvement of about 25–30% in the pairing computation over previous implementations. We also provide results for the MSP430X extension of the original family, which has new instructions. In particular, using the new 32-bit hardware multiplier available in some MSP430X models, we have achieved a further improvement of about 45% in the prime field multiplication and 20–30% in protocol timings. The combination of fast algorithms and improved hardware allows us to show that even the 128-bit level of security can be considered feasible for this platform.

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References

  1. Al-Daoud E., Mahmod R., Rushdan M., Kilicman A.: A new addition formula for elliptic curves over GF(2n). IEEE Trans. Comput. 51(8), 972–975 (2002). doi:10.1109/TC.2002.1024743

    Article  MathSciNet  Google Scholar 

  2. Aranha, D., Karabina, K., Longa, P., Gebotys, C., López, J.: Faster explicit formulas for computing pairings over ordinary curves. In: Advances in Cryptology—EUROCRYPT 2011. Lecture Notes in Computer Science, vol. 6632, pp. 48–68. Springer, Berlin (2011). doi:10.1007/978-3-642-20465-4_5

  3. Aranha D.F., Oliveira L.B., López J., Dahab R.: Efficient implementation of elliptic curve cryptography in wireless sensors. Adv. Math. Commun. 4(2), 169–187 (2011)

    Article  Google Scholar 

  4. Arène C., Lange T., Naehrig M., Ritzenthaler C.: Faster computation of the Tate pairing. J. Number Theory 131(5), 842–857 (2011). doi:10.1016/j.jnt.2010.05.013

    Article  MathSciNet  MATH  Google Scholar 

  5. Barreto P.S.L.M., Galbraith S., Ó hÉigeartaigh C., Scott M.: Efficient pairing computation on supersingular abelian varieties. Des. Codes Cryptogr. 42(3), 239–271 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Barreto, P.S.L.M., Naehrig, M.: Pairing-friendly elliptic curves of prime order. In: Selected Areas in Cryptography. Lecture Notes in Computer Science, vol.3897, pp. 319–331. Springer, Berlin (2006)

  7. Bernstein, D.: A software implementation of NIST P-224. In: Presentation at the 5th Workshop on Elliptic Curve Cryptography (ECC 2001) (2001)

  8. Bernstein, D., Lange, T.: Faster addition and doubling on elliptic curves. In: Advances in Cryptology—ASIACRYPT 2007. Lecture Notes in Computer Science, vol. 4833, pp. 29–50. Springer, Berlin (2008). doi:10.1007/978-3-540-76900-2_3

  9. Boneh D., Lynn B., Shacham H.: Short signatures from the Weil pairing. J. Cryptol. 17(4), 297–319 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Certicom Research: SEC 2: Recommended elliptic curve domain parameters version 1.0 (2000). http://www.secg.org/

  11. Comba P.G.: Exponentiation cryptosystems on the IBM PC. IBM Syst. J. 29(4), 526–538 (1990)

    Article  Google Scholar 

  12. Coppersmith D.: Fast evaluation of logarithms in fields of characteristic two. IEEE Trans. Inf. Theory 30(4), 587–594 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dudacek, K., Vavricka, V.: Experimental evaluation of the MSP430 microcontroller power requirements. In: The International Conference on “Computer as a Tool”—EUROCON, 2007, pp. 400–404 (2007)

  14. Dupont R., Enge A.: Provably secure non-interactive key distribution based on pairings. Discret. Appl. Math. 154(2), 270–276 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Fong K., Hankerson D., López J., Menezes A.: Field inversion and point halving revisited. IEEE Trans. Comput. 53(8), 1047–1059 (2004)

    Article  Google Scholar 

  16. Fuentes-Castañeda L., Knapp, E., Rodríguez-Henríquez, F.: Faster hashing to \({\mathbb{G}_2}\). In: Selected Areas in Cryptography—SAC 2011 (2011)

  17. Galindo, D., Roman, R., Lopez, J.: A killer application for pairings: Authenticated key establishment in underwater wireless sensor networks. In: Cryptology and Network Security. Lecture Notes in Computer Science, vol. 5339, pp. 120–132. Springer, Berlin (2008)

  18. Gallant, R.P., Lambert, R.J., Vanstone, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: Advances in Cryptology—CRYPTO 2001. Lecture Notes in Computer Science, vol. 2139, pp. 190–200. Springer, Berlin (2001)

  19. Gouvêa, C.P.L., López, J.: Software implementation of pairing-based cryptography on sensor networks using the MSP430 microcontroller. In: Progress in Cryptology—INDOCRYPT 2009. Lecture Notes in Computer Science, vol. 5922, pp. 248–262. Springer, Berlin (2009)

  20. Granger, R., Scott, M.: Faster squaring in the cyclotomic subgroup of sixth degree extensions. In: Public Key Cryptography—PKC 2010. Lecture Notes in Computer Science, vol. 6056, pp. 209–223. Springer, Berlin (2010)

  21. Großschädl, J.: TinySA: A security architecture for wireless sensor networks. In: Proceedings of the 2006 ACM CoNEXT conference, pp.55. ACM, New York (2006)

  22. Guajardo, J., Blümel, R., Krieger, U., Paar, C.: Efficient implementation of elliptic curve cryptosystems on the TI MSP430x33x family of microcontrollers. In: Public Key Cryptography. Lecture Notes in Computer Science, vol. 1992, pp. 365–382. Springer, Berlin (2001)

  23. Hankerson D., Menezes A., Vanstone S.: Guide to Elliptic Curve Cryptography. Springer, New York (2004)

    MATH  Google Scholar 

  24. Karabina, K.: Squaring in cyclotomic subgroups. Cryptology ePrint Archive, Report 2010/542 (2010). http://eprint.iacr.org/

  25. Karatsuba A., Ofman Y.: Multiplication of multidigit numbers on automata. Soviet Phys. Doklady 7, 595 (1963)

    Google Scholar 

  26. Knežević M., Vercauteren F., Verbauwhede I.: Faster interleaved modular multiplication based on Barrett and Montgomery reduction methods. IEEE Trans. Comput. 59(12), 1715–1721 (2010)

    Article  MathSciNet  Google Scholar 

  27. Law L., Menezes A., Qu M., Solinas J., Vanstone S.: An efficient protocol for authenticated key agreement. Des. Codes Cryptogr. 28, 119–134 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  28. Lim, C.H., Lee, P.J.: More flexible exponentiation with precomputation. In: Advances in Cryptology—CRYPTO’94. Lecture Notes in Computer Science, vol. 839, pp. 95–107. Springer, Berlin (1994)

  29. López, J., Dahab, R.: High-speed software multiplication in \({\mathbb{F}_{2^m}}\). In: Progress in Cryptology—INDOCRYPT 2000. Lecture Notes in Computer Science, vol. 1977, pp. 93–102. Springer, Berlin (2000)

  30. Miller V.S.: The Weil pairing, and its efficient calculation. J. Cryptol. 17, 235–261 (2004)

    Article  MATH  Google Scholar 

  31. Möller, B.: Algorithms for multi-exponentiation. In: Selected Areas in Cryptography. Lecture Notes in Computer Science, vol. 2259, pp. 165–180. Springer, Berlin (2001)

  32. Montgomery P.L.: Modular multiplication without trial division. Math. Comput. 44(170), 519–521 (1985)

    Article  MATH  Google Scholar 

  33. National Institute of Standards and Technology: Recommendation for key management (2007). http://www.itl.nist.gov

  34. National Institute of Standards and Technology: FIPS 186-3: Digital signature standard (DSS) (2009). http://www.itl.nist.gov

  35. Nogami, Y., Akane, M., Sakemi, Y., Kato, H., Morikawa, Y.: Integer variable χ-based Ate pairing. In: Pairing-Based Cryptography—Pairing 2008. Lecture Notes in Computer Science, vol. 5209, pp. 178–191. Springer, Berlin (2008)

  36. Oliveira L.B., Aranha D.F., Gouvêa C.P.L., Scott M., Câmara D.F., López J., Dahab R.: TinyPBC: pairings for authenticated identity-based non-interactive key distribution in sensor networks. Comput. Commun. 34(3), 485–493 (2010)

    Article  Google Scholar 

  37. Oliveira, L.B., Kansal, A., Gouvêa, C.P.L., Aranha, D.F., López, J., Priyantha, B., Goraczko, M., Zhao, F.: Secure-TWS: Authenticating node to multi-user communication in shared sensor networks. Comput. J. (2011). doi:10.1093/comjnl/bxr089

  38. Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: The 2000 Symposium on Cryptography and Information Security, Okinawa, Japan (2000)

  39. Schnorr C.P.: Efficient signature generation by smart cards. J. Cryptol. 4(3), 161–174 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  40. Scott, M., Benger, N., Charlemagne, M., Dominguez Perez, L.J., Kachisa, E.J.: On the final exponentiation for calculating pairings on ordinary elliptic curves. In: Pairing-Based Cryptography—Pairing 2009. Lecture Notes in Computer Science, vol. 5671. Springer, Berlin (2009)

  41. Scott, M., Szczechowiak, P.: Optimizing multiprecision multiplication for public key cryptography. Cryptology ePrint Archive, Report 2007/299 (2007). http://eprint.iacr.org/

  42. Solinas J.A.: Efficient arithmetic on Koblitz curves. Des. Codes Cryptogr. 19(2), 195–249 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  43. Szczechowiak, P., Kargl, A., Scott, M., Collier, M.: On the application of pairing based cryptography to wireless sensor networks. In: Proceedings of the second ACM conference on Wireless network security, pp. 1–12. ACM, New York (2009)

  44. Szczechowiak, P., Oliveira, L.B., Scott, M., Collier, M., Dahab, R.: NanoECC: Testing the limits of elliptic curve cryptography in sensor networks. In: Wireless Sensor Networks. Lecture Notes in Computer Science, vol. 4913. Springer, Berlin (2008)

  45. Vercauteren F.: Optimal pairings. IEEE Trans. Inf. Theory 56(1), 455–461 (2010)

    Article  MathSciNet  Google Scholar 

  46. Weber, D., Denny, T.: The solution of McCurley’s discrete log challenge. In: Advances in Cryptology—CRYPTO ’98. Lecture Notes in Computer Science, vol. 1462, pp. 458–471. Springer, Berlin (1998). doi:10.1007/BFb0055747

  47. Zhang, F., Safavi-Naini, R., Susilo, W.: An efficient signature scheme from bilinear pairings and its applications. In: Public Key Cryptography—PKC 2004. Lecture Notes in Computer Science, vol. 2947, pp. 277–290. Springer, Berlin (2004)

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Authors and Affiliations

  1. University of Campinas, Campinas, Brazil

    Conrado P. L. Gouvêa & Julio López

  2. Federal University of Minas Gerais, Belo Horizonte, Brazil

    Leonardo B. Oliveira

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  1. Conrado P. L. Gouvêa
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  2. Leonardo B. Oliveira
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  3. Julio López
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Correspondence to Conrado P. L. Gouvêa.

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Gouvêa, C.P.L., Oliveira, L.B. & López, J. Efficient software implementation of public-key cryptography on sensor networks using the MSP430X microcontroller. J Cryptogr Eng 2, 19–29 (2012). https://doi.org/10.1007/s13389-012-0029-z

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