Efficient Hardware Implementation of Modular Arithmetic and Group Operation Over Prime Field
Internet of Things and Cloud Computing
Volume 7, Issue 1, March 2019, Pages: 31-38
Received: May 5, 2019; Published: Jun. 15, 2019
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Authors
Sakib Absar, Department of Electrical and Electronic Engineering (EEE), Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh
Md Selim Hossain, Department of Electrical and Electronic Engineering (EEE), Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh
Yinan Kong, School of Engineering, Macquarie University, Sydney, NSW, Australia
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Abstract
The need for secure communication over the network has increased drastically over recent years, and Elliptic Curve Cryptography (ECC) carries out a significant role in moving secured information. In this work, a hardware implementation of modular arithmetic and group operations over the prime field for an Elliptic Curve Cryptography Processor (ECP) for an efficient security system is proposed. The modular addition or subtraction operation takes only one clock cycle and the modular multiplication, which is designed using the interleaved modular multiplication method, requires 257 clock cycles. For elliptic curve group operation separate point doubling (PD) and point addition (PA) architectures are implemented in Jacobean coordinates. These new architectures are simulated in a Xilinx ISE 14.7. After that, the architectures are implemented in Xilinx Virtex-7 field-programmable gate array (FPGA) with the VHDL language. Proposed modular arithmetic and group operations can be utilized to design an Elliptic Curve Point Multiplication (ECPM).
Keywords
Elliptic Curve Cryptography (ECC), Modular Arithmetic, Elliptic Curve Group Operation, Point Doubling (PD), Point Addition (PA), Field-Programmable Gate Array (FPGA)
To cite this article
Sakib Absar, Md Selim Hossain, Yinan Kong, Efficient Hardware Implementation of Modular Arithmetic and Group Operation Over Prime Field, Internet of Things and Cloud Computing. Vol. 7, No. 1, 2019, pp. 31-38. doi: 10.11648/j.iotcc.20190701.15
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