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An improved McEliece cryptosystem based on QC-MDPC code with compact key size

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Abstract

The McEliece cryptosystem based on quasi-cyclic moderate-density parity-check with adaptive chosen-ciphertext attack conversion is secure against information set decoding and message-resend attacks. However, it is vulnerable to reaction based key recovery attacks and cannot be implemented over the noise channel. To overcome this problem, we propose an improved McEliece cryptosystem based on quasi-cyclic quasi moderate-density parity-check (QC-QMDPC). In this cryptosystem, a stamp generation function which is based on the pseudorandom sequence is designed to resist the message-resend attack. The random channel noise is employed to enhance security. Furthermore, the upper bound of the density of QC-QMDPC code is proved for optimal efficiency. The index-based storage technique is proposed so that the key size can be reduced to approximately quadruple code length. The encoding and decoding algorithms are optimized to reduce the computational cost on the hardware platform. We analyze the performance of the proposed cryptosystem and compare it with other McEliece cryptosystems. The results show that the proposed cryptosystem is secure against critical attacks while keeping high error correction ability and efficiency.

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Availability of data and materials

The datasets used or analyzed during the current study are included in this manuscript.

Code availability

All the code used during the current study is available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the following projects and foundations: project ZR2019MF054 supported by Shandong Provincial Natural Science Foundation, the National Natural Science Foundation of China (No. 61902091) and Innovation Research Foundation of Harbin Institute of Technology (HIT.NSRIF.2020099), the Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-004), 2017 Weihai University Co-construction Project.

Funding

This work was supported by the following fundings: the Shandong Provincial Natural Science Foundation (No. ZR2019MF054), the National Natural Science Foundation of China (No. 61902091), the Innovation Research Foundation of Harbin Institute of Technology (HIT.NSRIF.2020099), the Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-004), 2017 Weihai University Co-construction Project.

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Authors and Affiliations

  1. School of Software, Northwestern Polytechnical University, Xi’an, 710000, China

    Jie Liu & Miao Zhang

  2. School of Computer Science and Technology, Harbin Institute of Technology, Weihai, 264209, China

    Jie Liu & Xiaojun Tong

  3. School of Information and Electrical Engineering, Harbin Institute of Technology, Weihai, 264209, China

    Zhu Wang

  4. Science and Technology on Information Assurance Laboratory, Beijing, 100072, China

    Jing Ma

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  1. Jie Liu
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Contributions

Under supervision by XT, JL performed the design of the scheme and the security analysis. ZW and MZ developed the experiment of performance analysis. JL and MZ prepared the writing of the draft. JM completed the writing-reviewing and edit. All authors read and contributed to the manuscript.

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Correspondence to Xiaojun Tong.

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Liu, J., Tong, X., Wang, Z. et al. An improved McEliece cryptosystem based on QC-MDPC code with compact key size. Telecommun Syst 80, 17–32 (2022). https://doi.org/10.1007/s11235-022-00881-7

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