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An ECC processor for IoT using Edwards curves and DFT modular multiplication

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Abstract

In this work, an elliptic curve cryptography (ECC) processor is proposed to be used in the Internet of Things (IoT) devices. The ECC processor is designed based on Edwards curves defined over the finite prime fields \(GF((2^{13}-1)^{13})\), \(GF((2^{17}-1)^{17})\), and \(GF((2^{19}-1)^{19})\). Modular multiplication in the proposed ECC processor is carried out in the frequency domain using a Discrete Fourier Transform (DFT) modular multiplier. Different base field adders and base field multipliers are designed and utilized in the design of the DFT modular multiplier. The ECC processor is described and functionally tested using the VHDL language and the simulation tool in the Xilinx ISE14.2. Furthermore, the ECC processor is synthesized using the synthesis tool in the Xilinx ISE14.2, targeting the Virtex-5 FPGA family. Our synthesis results show that the proposed ECC processor achieves higher speed with minor area penalty compared to the similar work in the literature.

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Acknowledgements

Alptekin Küpçü acknowledges support from TÜBİTAK, the Scientific and Technological Research Council of Turkey, project 119E088. Osama Al-Khaleel acknowledges support from JUST-Deanship of Research, project 20190201. Osama Al-Khaleel acknowledges the support from XILINX University Program to Jordan University of Science and Technology (JUST).

Funding

Alptekin Küpçü acknowledges support from TÜBİTAK, the Scientific and Technological Research Council of Turkey, project 119E088. Osama Al-Khaleel acknowledges support from JUST-Deanship of Research, project 20190201.

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Author notes

  1. Selcuk Baktır and Alptekin Küpçü have contributed equally to this work.

Authors and Affiliations

  1. Computer Engineering Department, Jordan University of Science and Technology, Irbid, 22110, Jordan

    Osama Al-Khaleel

  2. College of Engineering and Technology, American University of the Middle East, 54200, Egaila, Kuwait

    Selcuk Baktir

  3. Computer Science and Engineering, Koç University, Rumeli Feneri Yolu, Sarıyer, 34450, Istanbul, Turkey

    Alptekin Küpçü

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  1. Osama Al-Khaleel
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  2. Selcuk Baktir
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  3. Alptekin Küpçü
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All authors have been personally and actively involved in substantial work leading to the paper, and will take public responsibility for its content.

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Correspondence to Osama Al-Khaleel.

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The work presented in this paper is a valuable extension to our work presented in 12th International Conference on Information and Communication Systems (ICICS2021). In this journal version, we extend our proposal to cover higher security levels, modify our solution to also work over the finite prime fields \(GF((2^{17}-1)^{17})\) and \(GF((2^{19}-1)^{19})\) in addition to \(GF((2^{13}-1)^{13})\), and perform and report extended. performance and area measurements. The paper is not currently being considered for publication elsewhere. The paper reflects the authors’ own research and analysis in a truthful and complete manner. The results are appropriately placed in the context of prior and existing research. All sources used are properly disclosed (correct citation).

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Al-Khaleel, O., Baktir, S. & Küpçü, A. An ECC processor for IoT using Edwards curves and DFT modular multiplication. Cluster Comput 26, 1063–1075 (2023). https://doi.org/10.1007/s10586-022-03611-5

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