AN EFFICIENT RECONFIGURABLE SOS MONTGOMERY MULTIPLIER IN GF (P) USIGN FPGA DSP SLICES

Muhammed Nauman Qureshi, Muhammad Nadeem Sial, Nassar Ikram

Abstract

Montgomery Modular Multiplication in hardware is of great importance for the realisation of practical public key systems. Hence, an efficient implementation of modular exponentiation in terms of speed and resources in hardware is essential. This paper focuses on implementation of fully pipelined SOS based Montgomery Multiplication algorithm in Virtex-5 FPGA using DSP slices to achieve best area-speed trade off. Our implementation results and comparison with other Multipliers show that our Multiplier is comparable to known Montgomery Multipliers in terms of area-speed trade off.

References

  1. P., Montgomery, 1985. Modular multiplication without trial division. Mathematics of Computation. vol. 44, no. 170, pp.519-521.
  2. C.¸ K., Koc, T., Acar, and B., S., Kaliski, 1996. Analyzing and comparing Montgomery multiplication algorithms. IEEE Micro. vol. 16, no. 3, pp. 26-33.
  3. C., D., Walter, October 1999. Montgomery exponentiation needs no final subtraction. Electronic letters. vol. 35, no. 21, pp. 1831-1832.
  4. C., D., Walter, 1999. Montgomery's multiplication technique: How to make it smaller and faster. In C.¸ K., Koc and C., Paar, editors, Proceedings of the 1st International Workshop on Cryptographic Hardware and Embedded Systems (CHES), Lecture Notes in Computer Science, Springer-Verlag. no. 1717, pp. 80-93.
  5. Virtex-5 XtremeDSP Design Considerations User Guide, April 14, 2006. V1.0, UG193, www.xilinx.com.
  6. C., McIvor, M., McLoone, J., V., McCanny, A., Daly, and W., Marnane, 2003. Fast Montgomery modular multiplication and RSA cryptographic processor architectures. In Proceedings of the 37th Annual Asilomar Conference on Signals, Systems and Computers. pp. 379-384.
  7. Nele., Mentens, July, 2007. Secure and Efficient Coprocessor Design for Cryptographic Applications on FPGAs. PhD thesis. ISBN 978-90-5682-843-1.
  8. K., Kelley and D., Harris, 2005. Parallelized very high radix scalable Montgomery multipliers. In Conference Record of the Thirty-Ninth Asilomar Conference on Signals, Systems and Computers. pp. 1196-1200.
  9. C., McIvor, M., McLoone, and J., V., McCanny, 2004. FPGA Montgomery multiplier architectures - a comparison. In Proceedings of the 12th IEEE Symposium on Field-Programmable Custom Computing Machines (FCCM), IEEE Computer Society. pp. 279-282.
  10. K., Manochehri and S., Pourmozafari, 2004. Fast montgomery modular multiplication by pipelined CSA architecture. In Proceedings of the International Conference on Microelectronics (ICM). pp. 144-147.
  11. D., N., Amanor, V., Bunimov, C., Paar, J., Pelzl, and M., Schimmler, 2005. Efficient hardware architectures for modular multiplication on FPGAs. In Proceedings of the 15th International Conference on Field Programmable Logic and Applications (FPL), IEEE. pp. 539-542.
  12. V., Bunimov, M., Schimmler, and B., Tolg, 2002. A complexity-effective version of Montgomery's algorithm. In Proceedings of the Workshop on Complexity Effective Designs (WCED).
  13. L., Batina, G., Bruin-Muurling, and S., B., Ors, 2004. Flexible hardware design for RSA and elliptic curve cryptosystems. In T. Okamoto, editor, Proceedings of the RSA Conference - Topics in Cryptography (CTRSA), Lecture Notes in Computer Science SpringerVerlag. vol. 2964, pp. 250-263.
  14. Xilinx Virtex-4 Handbook. August 2, 2004.
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Paper Citation


in Harvard Style

Nauman Qureshi M., Nadeem Sial M. and Ikram N. (2008). AN EFFICIENT RECONFIGURABLE SOS MONTGOMERY MULTIPLIER IN GF (P) USIGN FPGA DSP SLICES . In Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008) ISBN 978-989-8111-59-3, pages 355-358. DOI: 10.5220/0001917303550358


in Bibtex Style

@conference{secrypt08,
author={Muhammed Nauman Qureshi and Muhammad Nadeem Sial and Nassar Ikram},
title={AN EFFICIENT RECONFIGURABLE SOS MONTGOMERY MULTIPLIER IN GF (P) USIGN FPGA DSP SLICES},
booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)},
year={2008},
pages={355-358},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001917303550358},
isbn={978-989-8111-59-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2008)
TI - AN EFFICIENT RECONFIGURABLE SOS MONTGOMERY MULTIPLIER IN GF (P) USIGN FPGA DSP SLICES
SN - 978-989-8111-59-3
AU - Nauman Qureshi M.
AU - Nadeem Sial M.
AU - Ikram N.
PY - 2008
SP - 355
EP - 358
DO - 10.5220/0001917303550358