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Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance.


Mohammad Alkhatib, and Jaafar, Azmi and Md Said, Mohamad Rushdan and Ahmad Zukarnain, Zuriati (2012) Parallelizing GF (p) montgomery elliptic curve crypto-system operations to improve security and performance. In: 3rd International Conference on Mechanical Aerospace Engineering (ICMAE 2012), 7-8 July 2012, Paris. (pp. 1906-1911).


The elliptic curve crypto-system (ECC) performs two levels of computations, lower point operations, and upper scalar multiplication levels. The use of usual serial design and affine coordinates to apply ECC computations increases the time delay and weaken the security of the crypto-system against simple power attack (SPA). This work combines the inherited parallelism in both computation levels for GF (p) Montgomery ECC to improve performance and enhance the immunity of the ECC against SPA. Moreover, projective coordinates were used to apply ECC operations to eliminate the time-consuming inversion operation. In order to increase the speed even further, this paper proposes to use known NAF algorithm for scalar multiplication, as well as Montgomery multiplier to perform multiplication operations. Hardware implementations with target FPGA for GF (p) Montgomery ECC are also presented. The best performance level was achieved when parallelizing Montgomery ECC computations to eight parallel multipliers (PM) using homogeneous coordinates. Such strategy, although it requires extra resources, is worth considering due to its attractive security and performance conclusions.

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Additional Metadata

Item Type: Conference or Workshop Item (Paper)
Divisions: Faculty of Computer Science and Information Technology
Institute for Mathematical Research
Notes: Full text are available at Special Collection Division Office
Keywords: Elliptic curve crypto-system; Projective coordinates; NAF algorithm; Montgomery multipliers; Parallelization level.
Depositing User: Erni Suraya Abdul Aziz
Date Deposited: 28 Feb 2014 10:21
Last Modified: 08 Apr 2014 01:06
URI: http://psasir.upm.edu.my/id/eprint/27312
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