Open Access Open Access  Restricted Access Subscription or Fee Access

GF (2m) Based Low Complexity Multiplier for Elliptic Curve Cryptography Systems

K. Rajadurga, S. Ram Kumar

Abstract


This study presents a low complexity multiplier for elliptic curve cryptography system over the GF (2m). One of the basis of polynomial basis in Galois field is used to design the cryptography system. This paper presents an area-time efficient systolic structure for multiplication to the elliptic curve cryptography (ECC).  Elliptic curve cryptography requires smaller key size, high speed and low bandwidth. It is provide the same security level like RSA in public key cryptography. Systolic structures are used to design the proposed multipliers. This proposed multipliers have low hardware requirements and regular structures; and they are suitable for VLSI implementations. The proposed design provides less area-delay and power-delay complexities over the existing designs. This low complexity multiplier based elliptic curve cryptography will be implemented using FPGA device.


Keywords


Galois Field, Polynomial Basis Multiplier, Elliptic Curve Cryptography, Systolic Structure

Full Text:

PDF

References


S. Talapatra, H. Rahaman, and J. Mathew, “Low complexity digit serial systolic montgomery multipliers for special class of GF (2m),” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 18, no. 5, pp. 847–852, May 2010.

P. K. Meher, “Systolic and non-systolic scalable modular designs of finite field multipliers for Reed-Solomon Codec,” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 17, no. 6, pp. 747–757, Jun. 2009.

H. Wu, “Bit-parallel polynomial basis multiplier for new classes of finite fields,” IEEE Trans. Computers, vol. 57, no. 8, pp. 1023–1031,Aug. 2008

H. Fan and M. A. Hasan, “Relationship between GF (2m) Montgomery and shifted polynomial basis multiplication algorithms,” IEEE Trans. Computers, vol. 55, no. 9, pp. 1202–1206, Sep. 2006.

C. H. Kim, C.-P. Hong, and S. Kwon, “A digit-serial multiplier for finite field GF (2m),” IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 13, no. 4, pp. 476–483, 2005

Y.-R. Ting, E.-H. Lu, and Y.-C. Lu, “Ringed bit-parallel systolic multipliersover a class of fields GF (2m),” Integr., VLSI J., vol. 38, no. 4,pp. 571–578, 2005.

C.-Y. Lee, E.-H. Lu, and J.-Y. Lee, “Bit-parallel systolic multipliers for GF (2m) fields defined by all-one and equally spaced polynomials,”IEEE Trans. Computers, vol. 50, no. 6, pp. 385–393, May 2001.

B. Sunar and C. K. Koc, “Mastrovito multiplier for all trinomials,” IEEE Trans. Comput., vol. 48, no. 5, pp. 522–527, May 1999.

C. Paar, “Low complexity parallel multipliers for Galois fields GF (2m) based on special types of primitive polynomials,” in Proc. IEEE Int. Symp. Inform. Theory, 1994, p. 98.

S. Fenn, M.G. Parker,M. Benaissa, and D. Taylor, “Bit-serial multiplication In GF (2m) using all-one polynomials,” IEE Proc. Com. Digit. Tech., vol. 144, no. 6, pp. 391–393, 1997.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.