Journal of information and communication convergence engineering

  • 제12권3호
  • /
  • Pages.145-153
  • /
  • 2014
  • /
  • 2234-8255(pISSN)
  • /
  • 2234-8883(eISSN)
한국정보통신학회 (The Korea Institute of Information and Commucation Engineering)
권호 표지
DOI QR코드

DOI QR Code

Study of Modular Multiplication Methods for Embedded Processors

  • Seo, Hwajeong (Department of Computer Engineering, Pusan National University) ;
  • Kim, Howon (Department of Computer Engineering, Pusan National University)
  • 투고 : 2014.03.25
  • 심사 : 2014.06.25
  • 발행 : 2014.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The improvements of embedded processors make future technologies including wireless sensor network and internet of things feasible. These applications firstly gather information from target field through wireless network. However, this networking process is highly vulnerable to malicious attacks including eavesdropping and forgery. In order to ensure secure and robust networking, information should be kept in secret with cryptography. Well known approach is public key cryptography and this algorithm consists of finite field arithmetic. There are many works considering high speed finite field arithmetic. One of the famous approach is Montgomery multiplication. In this study, we investigated Montgomery multiplication for public key cryptography on embedded microprocessors. This paper includes helpful information on Montgomery multiplication implementation methods and techniques for various target devices including 8-bit and 16-bit microprocessors. Further, we expect that the results reported in this paper will become part of a reference book for advanced Montgomery multiplication methods for future researchers.

키워드

참고문헌

  1. P. G. Comba, "Exponentiation cryptosystems on the IBM PC," IBM Systems Journal, vol. 29, no. 4, pp. 526-538, 1990. https://doi.org/10.1147/sj.294.0526
  2. N. Gura, A. Patel, A. Wander, H. Eberle, and S. C. Shantz, "Comparing elliptic curve cryptography and RSA on 8-bit CPUs," in Cryptographic Hardware and Embedded Systems-CHES 2004. Heidelberg: Springer, pp. 119-132, 2004.
  3. M. Hutter and E. Wenger, "Fast multi-precision multiplication for public-key cryptography on embedded microprocessors," in Cryptographic Hardware and Embedded Systems-CHES 2011. Heidelberg: Springer, pp. 459-474, 2011.
  4. H. Seo and H. Kim, "Multi-precision multiplication for public-key cryptography on embedded microprocessors," in Information Security Applications. Heidelberg: Springer, pp. 55-67, 2012.
  5. P. Y. Hsieh and C. S. Laih, "An exception handling model and its application to the multiple-precision integer library," Doctoral dissertation, 2003.
  6. M. Scott and P. Szczechowiak, Optimizing multiprecision multiplication for public key cryptography [Internet], Available: https://eprint.iacr.org/2007/299.pdf.
  7. Y. Lee, I. H. Kim, and Y. Park, "Improved multi-precision squaring for low-end RISC microcontrollers," Journal of Systems and Software, vol. 86, no. 1, pp. 60-71, 2013. https://doi.org/10.1016/j.jss.2012.06.074
  8. H. Seo, Z. Liu, J. Choi, and H. Kim, "Multi-precision squaring for public-key cryptography on embedded microprocessors," in Progress in Cryptology-INDOCRYPT 2013. Heidelberg: Springer, pp. 227-243, 2013.
  9. P. L. Montgomery, "Modular multiplication without trial division," Mathematics of Computation, vol. 44, no. 170, pp. 519-521, 1985. https://doi.org/10.1090/S0025-5718-1985-0777282-X
  10. Z. Liu and J. Grossschadl, "New speed records for montgomery modular multiplication on 8-bit AVR microcontrollers," in Progress in Cryptology-AFRICACRYPT 2014. Heidelberg: Springer, pp. 215-234, 2014.
  11. J. Grossschadl, "TinySA: a security architecture for wireless sensor networks," in Proceedings of the 2006 ACM Conference on Emerging Network Experiment and Technology (CoNEXT), Lisboa, Portugal, article no. 55, 2006.
  12. D. Chu, J. Grossschadl, Z. Liu, V. Muller, and Y. Zhang, "Twisted edwards-form elliptic curve cryptography for 8-bit AVR-based sensor nodes," in Proceedings of the 1st ACM Workshop on Asia Public-Key Cryptography, Hangzhou, China, pp. 39-44, 2013.
  13. J. Grossschadl, M. Hudler, M. Koschuch, M. Kruger, and A. Szekely, "Smart elliptic curve cryptography for smart dust," in Quality, Reliability, Security and Robustness in Heterogeneous Networks. Heidelberg: Springer, pp. 623-634, 2012.
  14. J. L. Hill and D. E. Culler, "Mica: a wireless platform for deeply embedded networks," IEEE Micro, vol. 22, no. 6, pp. 12-24, 2002.
  15. A. Liu and P. Ning, "TinyECC: a configurable library for elliptic curve cryptography in wireless sensor networks," in Proceedings of the International Conference on Information Processing in Sensor Networks, St. Louise, MO, pp. 245-256, 2008.
  16. CertiVox Corporation, CertiVox MIRACL SDK source code, http://www.certivox.com.
  17. C. P. Gouvea, L. B. Oliveira, and J. Lopez, "Efficient software implementation of public-key cryptography on sensor networks using the MSP430X microcontroller," Journal of Cryptographic Engineering, vol. 2, no. 1, pp. 19-29, 2012. https://doi.org/10.1007/s13389-012-0029-z
  18. P. Szczechowiak, A. Kargl, M. Scott, and M. Collier, "On the application of pairing based cryptography to wireless sensor networks," in Proceedings of the 2nd ACM Conference on Wireless Network Security, Zurich, Switzerland, pp. 1-12, 2009.
  19. C. P. Gouvea and J. Lopez, "Software implementation of pairing-based cryptography on sensor networks using the MSP430 microcontroller," in Progress in Cryptology-INDOCRYPT 2009. Heidelberg: Springer, pp. 248-262, 2009.
  20. H. Seo, K. A. Shim, and H. Kim, "Performance enhancement of TinyECC based on multiplication optimizations," Security and Communication Networks, vol. 6, no. 2, pp. 151-160, 2013. https://doi.org/10.1002/sec.422
  21. L. Uhsadel, A. Poschmann, and C. Paar, "Enabling full-size public-key algorithms on 8-bit sensor nodes," in Security and Privacy in Ad-hoc and Sensor Networks. Heidelberg: Springer, pp. 73-86, 2007.
  22. Y. Zhang and J. Grossschadl, "Efficient prime-field arithmetic for elliptic curve cryptography on wireless sensor nodes," in Proceedings of the 1st International Conference on Computer Science and Network Technology (ICCSNT), Harbin, China, pp. 459-466, 2011.
  23. Z. Liu, J. Grossschadl, and I. Kizhvatov, "Efficient and side-channel resistant RSA implementation for 8-bit AVR microcontrollers," in Proceedings of the 1st International Workshop on the Security of the Internet of Things, Tokyo, Japan, pp. 1-10, 2010.
  24. H. Seo, Y. Lee, H. Kim, T. Park, and H. Kim, "Binary and prime field multiplication for public key cryptography on embedded microprocessors," Security and Communication Networks, vol. 7, no. 4, pp. 774-787, 2014. https://doi.org/10.1002/sec.779