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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 862508, 7 pages
http://dx.doi.org/10.1155/2013/862508
Research Article

A Novel Elliptic Curve Scalar Multiplication Algorithm against Power Analysis

Shanghai Jiao Tong University, Shanghai 200240, China

Received 13 November 2012; Revised 10 March 2013; Accepted 12 March 2013

Academic Editor: Jun-Juh Yan

Copyright © 2013 Hongming Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. N. Koblitz, “Elliptic curve cryptosystems,” Mathematics of Computation, vol. 48, no. 177, pp. 203–209, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. V. S. Miller, “Use of elliptic curves in cryptography,” in Advances in Cryptology: Proceedings of Crypto '85, vol. 218 of Lecture Notes in Computer Science, pp. 417–426, Springer, Berlin, Germany, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. K. A. Shim and S. S. Woo, “Cryptanalysis of tripartite and multi-party authenticated key agreement protocols,” Information Sciences, vol. 177, no. 4, pp. 1143–1151, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. L. Wang, Z. Cao, X. Li, and H. Qian, “Simulatability and security of certificateless threshold signatures,” Information Sciences, vol. 177, no. 6, pp. 1382–1394, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. Cohen, A. Miyaji, and T. Ono, “Efficient elliptic curve exponentiation using mixed coordinates,” in Advances in Cryptology (ASIACRYPT '98), vol. 1514 of Lecture Notes in Computer Science, pp. 51–65, Springer, Berlin, Germany, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. Hankerson, A. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography, Springer Professional Computing, Springer, New York, NY, USA, 2004. View at Zentralblatt MATH · View at MathSciNet
  7. P. Kocher, “Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other system,” in Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO '96), vol. 1109 of Lecture Notes in Computer Science, pp. 104–113, Springer, 1996.
  8. P. Kocher, J. Jaffe, and B. Jun, “Differential power analysis,” in Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology (CRYPTO '99), vol. 1666 of Lecture Notes in Computer Science, pp. 388–397, Springer, 1999.
  9. T. Izu and T. Takagi, “A fast parallel elliptic curve multiplication resistant against side channel attacks,” in Public Key Cryptography (PKC 2002), vol. 2274 of Lecture Notes in Computer Science, pp. 280–296, Springer, 2002.
  10. J. Coron, “Resistance against differential power analysis for elliptic curve cryptosystems,” in Proceedings of the 1st International Workshop on Cryptographic Hardware and Embedded Systems (CHES '99), vol. 1717 of Lecture Notes in Computer Science, pp. 292–302, Springer, 1999.
  11. E. Oswald and M. Aigner, “Randomized addition-subtraction chains as a countermeasure against power attacks,” in Proceedings of the 3rd International Workshop on Cryptographic Hardware and Embedded Systems (CHES '01), vol. 2001 of Lecture Notes in Computer Science, pp. 39–50, Springer, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. B. Moller, “Securing elliptic curve point multiplication against side-channel attacks,” in Proceedings of the 4th International Information Security Conference (ISC '01), vol. 2200 of Lecture Notes in Computer Science, pp. 324–334, Springer, October 2001. View at Publisher · View at Google Scholar
  13. M. K. Lee, “SPA-resistant simultaneous scalar multiplication,” in Proceedings of the International Conference on Computational Science and Its Applications (ICCSA '05), vol. 3481, pp. 314–321, Singapore, May 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. M. Ciet and M. Joye, “(virtually) Free randomization technique for elliptic curve cryptography,” in Proceedings of the 5th International Conference on Information and Communications Security (ICICS '03), vol. 2836, pp. 348–359, 2003. View at Publisher · View at Google Scholar
  15. D. Liu and Z. Tan Y Dai, “New elliptic curve multi-scalar multiplication algorithm for a pair of integers to resist SPA,” in Proceedings of the 4th International Conference on Information Security and Cryptology (Inscrypt '08), vol. 5487 of Lecture Notes in Computer Science, pp. 253–264, Springer, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  16. N. Zhang, Z. Chen, and G. Xiao, “Efficient elliptic curve scalar multiplication algorithms resistant to power analysis,” Information Sciences, vol. 177, no. 10, pp. 2119–2129, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. Y. Liardet and N. P. Smart, “Preventing SPA/DPA in ECC systems using the Jacobi form,” in Proceedings of the 3rd International Workshop on Cryptographic Hardware and Embedded Systems (CHES '01), vol. 2162 of Lecture Notes in Computer Science, pp. 391–401, Springer, May 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Advances in Elliptic Curve Cryptography, Cambridge University Press, Cambridge, UK, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  19. ANSI X9.62:2005, Public Key Cryptography for the Financial Service Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA), American National Standards Institute, 2005.
  20. ANSI X9.63:2001, Public Key Cryptography for the Financial Service Industry: Key Agreement and Key Transport Using Elliptic Curve Cryptography, American National Standards Institute, 2001.
  21. A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone, Handbook of Applied Cryptography, CRC Press, Boca Raton, Fla, USA, 1997. View at MathSciNet
  22. J. Fan and I. Verbauwhede, “An Updated survey on secure ECC implementations: attacks, countermeasures and cost,” in Cryptography and Security: From Theory to Applications, vol. 6805 of Lecture Notes in Computer Science, pp. 265–282, Springer, 2012.
  23. IEEE Std 1363-2000, IEEE Standard Specifications for Public-Key Cryptography, Institute of Electrical and Electronics Engineers, New York, NY, USA, 2000. View at Publisher · View at Google Scholar
  24. C. H. Lim and H. S. Hwang, “Fast implementation of elliptic curve arithmetic in GF(Pn),” in Proceedings of the 3rd International Workshop on Practice and Theory in Public Key Cryptosystem (PKC '00), vol. 1751 of Lecture Notes in Computer Science, pp. 405–421, Springer, January 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet