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Polynomial-Time Key-Recovery Attacks Against NTRUReEncrypt from ASIACCS’15

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Abstract

In ASIACCS 2015, Nuñez, et al. proposed a proxy re-encryption scheme, named NTRUReEncrypt, based on NTRU, which allows a proxy to translate ciphertext under the delegator’s public key into a re-encrypted ciphertext that can be decrypted correctly by delegatee’s private key. Because of the potential resistance to quantum algorithm, high efficiency and various applications in real life, NTRUReEncrypt has drawn lots of attention and its security has been widely discussed and analyzed. In PQCrypto2019, Liu, et al. proposed two key recovery attacks against it. However, their first attack heavily relies on a weaken decryption oracle, and the second attack needs to collect about 260 ciphertexts from the same message by theoretical analysis, which makes both of the attacks unrealistic. In this paper, inspired by the broadcast attack against NTRU, the authors find out that for NTRUReEncrypt the delegator and the delegatee can efficiently recover each other’s private key in polynomial time without any unrealistic assumptions. In addition, the authors also show how to fix NTRUReEncrypt to resist the proposed attacks. As a by-product, the authors also show how to commit broadcast attacks against NTRU 2001 with even dg, which was thought infeasible before.

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Authors and Affiliations

  1. School of Cyber Science and Technology, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, China

    Zhen Liu

  2. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

    Yanbin Pan & Jinwei Zheng

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China

    Yanbin Pan & Jinwei Zheng

Authors
  1. Zhen Liu
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  2. Yanbin Pan
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  3. Jinwei Zheng
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Corresponding author

Correspondence to Jinwei Zheng.

Ethics declarations

PAN Yanbin is a youth editorial board member for Journal of Systems Science & Complexity and was not involved in the editorial review or the decision to publish this article. The authors declare that there are no competing interests.

Additional information

This research was supported by National Key Research and Development Program of China under Grant No. 2018YFA0704705, the National Natural Science Foundation of China under Grant Nos. 62032009, 12201193, and 12226006, the Innovation Program for Quantum Science and Technology under Grant No. 2021ZD0302902, the Innovation Group Project of the Natural Science Foundation of Hubei Province of China under Grant No. 2023AFA021, and the Science and Technology Research Program of Education Department of Hubei Province under Grant No. Q20221008.

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Liu, Z., Pan, Y. & Zheng, J. Polynomial-Time Key-Recovery Attacks Against NTRUReEncrypt from ASIACCS’15. J Syst Sci Complex 37, 1308–1325 (2024). https://doi.org/10.1007/s11424-024-2426-7

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  • DOI: https://doi.org/10.1007/s11424-024-2426-7

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