Paper 2021/152

Hybrid Dual Attack on LWE with Arbitrary Secrets

Lei Bi, Xianhui Lu, Junjie Luo, Kunpeng Wang, and Zhenfei Zhang


In this paper, we study the {\em hybrid dual attack} over Learning with Errors (LWE) problems for {\em any} secret distribution. Prior to our work, hybrid attacks are only considered for sparse and/or small secrets. A new and interesting result from our analysis shows that for most cryptographic use cases a hybrid dual attack outperforms a standalone dual attack, regardless of the secret distribution. We formulate our results into a framework of predicting the performance of the hybrid dual attacks. We also present a few tricks that further improve our attack. To illustrate the effectiveness of our result, we re-evaluate the security of {\em all} LWE related proposals in round 3 of NIST's post-quantum cryptography process, and improve the state-of-the-art cryptanalysis results by 2-14 bits, under the BKZ-core-SVP model.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
Learning with ErrorsLattice-based CryptographyCryptanalysisDual AttackHybrid attackNIST PQC
Contact author(s)
bilei121 @ outlook com
2021-02-25: last of 2 revisions
2021-02-12: received
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Creative Commons Attribution


      author = {Lei Bi and Xianhui Lu and Junjie Luo and Kunpeng Wang and Zhenfei Zhang},
      title = {Hybrid Dual Attack on LWE with Arbitrary Secrets},
      howpublished = {Cryptology ePrint Archive, Paper 2021/152},
      year = {2021},
      note = {\url{}},
      url = {}
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