58
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Hardware realization of fast elliptic curve point multiplication using balanced ternary representation and pre-computation over GF(p)

&
Pages 141-161 | Received 01 Aug 2014, Published online: 18 May 2016

References

  • B. Schneier, Applied Cryptography: Protocols, Algorithms, and Source Code in C, 2nd ed. New York: Wiley, 1996.
  • A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography. Boca Raton, FL: CRC Press, 1997.
  • N. Koblitz, Elliptic curve cryptosystems, Math. Comput., Vol. 48, pp. 203–209, 1987. doi: 10.1090/S0025-5718-1987-0866109-5
  • V.S. Miller, “Use of elliptic curve in cryptography,” in Proc. Crypto, pp. 417–426, 1986.
  • Darrel Hankerson, Alfred Menezes and Scott Vanstone, “Guide to Elliptic Curve Cryptography”, Springer-Verlag, 2004.
  • Santosh Ghosh, Monjur Alam, Indranil Sen Gupta and Dipanwita Roy Chowdhury, “A Robust GF(p) Parallel Arithmetic Unit for Public Key Cryptography,” IEEE International Euromicro Conference on Digital System Design Architectures, Methods and Tools, pp. 109–115, 2007.
  • G. Orlando and C. Paar, “A scalable GF(p) elliptic curve processor ar- chitecture for programmable hardware,” in: Cryptograpic Hardware and Embedded Systems (CHES2001), LNCS 2162, pp 348–363, 2001.
  • de Dormole G.M. and Quisquater J.J., “High-speed hardware imple- mentations of Elliptic Curve Cryptography: A survey,” Journal of Systems Architecture, Vol 53, pp. 72–84, 2007. doi: 10.1016/j.sysarc.2006.09.002
  • Ayantika Chatterjee and Indranil Sengupta, “FPGA implementation of binary edwards curve using ternary representation”, Proceedings of the 21st edition of the Great lakes symposium on VLSI, ACM, pp. 73–78, 2011.
  • Vassil Dimitrov, Laurent Imbert, and Pradeep Kumar Mishra, “Efficient and Secure Elliptic Curve Point Multiplication using Double-Base Chains,” 11th International Conference on the Theory and Application of Cryptology and Information Security, LNCS 3788, pp 59–78, 2005.
  • Vinay S. Iyengar, “Novel elliptic curve scalar multiplication algorithms for faster and safer public-key cryptosystems”, International Journal on Cryptography and Information Security(IJCIS), Vol 2, pp.57–66,2012. doi: 10.5121/ijcis.2012.2305
  • H. Cohen, G. Frey, R.M. Avanzi, C. Doche, T. Lange, K. Nguyen and F. Vercauteren, “Handbook of elliptic and hyperelliptic curve cryptography”, Discrete Mathematics and its Applications, Vol. 34, Chapman & Hall/CRC, 2005.
  • I.F. Blake, G. Seroussi, and N.P. Smart, “Elliptic curves in cryptography”, Number 256 in London mathematical society lecture note series. Cambridge university press, 1999.
  • C.J. McIvor, M. McLoone, and J.V. McCanny, “Hardware elliptic curve cryptographic processor over GF(p),” IEEE Trans. Circuits Syst. I, Reg. Papers, Vol. 53, no. 9, pp. 1946–1957, Sep. 2006.
  • J.Y. Lai and C.T. Huang, “High-throughput cost-effective dual-field processors and the design framework for elliptic curve cryptography,” IEEE trans. on VLSI Systems, Vol. 16, pp. 1567–1580, 2008. doi: 10.1109/TVLSI.2008.2001239
  • J.W. Lee, J.H. Hsiao, H.C. Chang, and C.Yi. Lee, “An efficient DPA countermeasure with randomized Montgomery operations for DF-ECC Processor”, IEEE Trans. On Circuits and Systems—II: Vol. 59, pp. 287–291, 2012. doi: 10.1109/TCSII.2012.2190857
  • J.W. Lee, S.C. Chung, H.C. Chang and C.Y. Lee, “Efficient power-analysis-resistant dual-field elliptic curve cryptographic processor using heterogeneous dual-processing element architecture,” IEEE Trans. on VLSI Systems, Vol. 22, pp. 49–61, 2013. doi: 10.1109/TVLSI.2013.2237930
  • Virtex-5 Platform FPGAs: Complete Data sheet http://www.xilinx.com/Publications/DS100.pdf

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.