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Secure one-way relaying scheme based on random difference family (RDF) lattice codes

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Abstract

In this paper, we present a one-way relaying scheme in which two wireless nodes create an information flow to each other via a single decode-and-forward (DF) relay. We consider an additional secrecy constraint for protection against an honest-but-curious relay. Indeed, while the relay should decode the source message, it should be fully ignorant about the message content. We provide a secure lattice coding strategy based on random difference families (RDF) lattice codes for unidirectional Gaussian relay channels. RDF lattice codes are carved from infinite RDF lattices using a shaping algorithm. By RDF lattice we mean a Construction A lattice with a QC-LDPC code, which is obtained from random difference families, as underlying code. Due to the existence of low-overhead encoding and decoding algorithms, these lattice codes can be implemented practically in high dimensions. Our proposed scheme combines a new Rao–Nam-like encryption with a new DF relaying scheme for RDF lattice codes. Security analysis of the scheme against chosen-plaintext attacks like differential attack and other recent attacks on the Rao–Nam-like schemes are provided. We show that the proposed scheme resists against all variants of differential cryptanalysis. To the best of our knowledge, the proposed scheme is the first in its type and according to our simulation results, it improves the error performance, efficiency and security at the same time, compared to its counterparts.

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Acknowledgements

The authors are grateful to the editor and the referees for their very meticulous reading of this manuscript. Their suggestions were very helpful in creating the improved final version.

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Authors and Affiliations

  1. Electronics Research Institute, Sharif University of Technology, Tehran, P. O. Box: 11155-8639, Iran

    Khadijeh Bagheri

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran

    Hassan Khodaiemehr

  3. Department of Computer Science and Statistics, Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, 16315-1618, Iran

    Hassan Khodaiemehr

  4. Electronics Research Institute, Sharif University of Technology, Tehran, P. O. Box: 11155-8639, Iran

    Taraneh Eghlidos

  5. School of Mathematics and Statistics, Carleton University, Ottawa, Canada

    Daniel Panario

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  1. Khadijeh Bagheri
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  2. Hassan Khodaiemehr
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  3. Taraneh Eghlidos
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  4. Daniel Panario
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Correspondence to Hassan Khodaiemehr.

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The research of the second author was supported in part by a grant from IPM (No. 1400050115), and the fourth author was supported by NSERC of Canada. Part of the results of this paper have been presented at the 15th international ISC conference (ISCISC 2018) [18].

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Bagheri, K., Khodaiemehr, H., Eghlidos, T. et al. Secure one-way relaying scheme based on random difference family (RDF) lattice codes. Wireless Netw 27, 4615–4634 (2021). https://doi.org/10.1007/s11276-021-02753-5

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