## High-Performance FPGA Implementation of Modular Inversion over F_256 for Elliptic Curve Cryptography

2015 IEEE International Conference on Data Science and Data Intensive Systems (DSDIS) (2015)

Sydney, Australia

Dec. 11, 2015 to Dec. 13, 2015

ISBN: 978-1-5090-0214-6

pp: 169-174

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/DSDIS.2015.47

ABSTRACT

Modular Inversion over a prime field is an important operation for public-key cryptographic applications. It is the most crucial operation to speed up the calculation of an elliptic curve crypto-processor (ECC) when affine coordinates are used. In this work, the main goal is to implement a fast, high-performance modular inversion for ECC using field-programmable gate-array (FPGA) technology. A binary inversion algorithm in VHDL has been used for this efficient implementation. Timing simulation shows that the delay for one modular inversion operation in a modern Xilinx Virtex-7 FPGA is only 2.329 us at the maximum frequency of 146.389 MHz. We have implemented an area-efficient design which takes a small amount of resources on the FPGA and needs only 1480 slices. To the best of the authors' knowledge, the proposed modular inversion over F_256 provides a better performance than the available hardware implementations in terms of the area and the timing.

INDEX TERMS

Elliptic curve cryptography, Hardware, Field programmable gate arrays, Elliptic curves, Algorithm design and analysis

CITATION

M. S. Hossain and Y. Kong, "High-Performance FPGA Implementation of Modular Inversion over F_256 for Elliptic Curve Cryptography,"

*2015 IEEE International Conference on Data Science and Data Intensive Systems (DSDIS)*, Sydney, Australia, 2015, pp. 169-174.

doi:10.1109/DSDIS.2015.47

CITATIONS