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Polynomial-Time Key-Recovery attacks Against NTRURe Encrypt from ASIACCS'15

Journal of Systems Science & Complexity 2024年第3期37卷 1308-1325页

作者： LIU Zhen PAN Yanbin ZHENG Jinwei School of Cyber Science and Technology Hubei Key Laboratory of Applied MathematicsHubei UniversityWuhan 430062China Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China

In ASIACCS 2015, Nu nez, et al. proposed a proxy re-encryption scheme, named NTRURe Encrypt, 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,NTRURe Encrypt 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 260ciphertexts 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 NTRURe Encrypt 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 NTRURe Encrypt 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.

关键词： broadcast attack key recovery NTRU NTRUReEncrypt

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