In this paper, we study the hybrid dual attack over learning with errors (LWE) problems for 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 all LWE related proposals in round 3 of NIST’s post-quantum cryptography process, and improve the state-of-the-art cryptanalysis results by 2-15 bits, under the BKZ-core-SVP model.
CITATION STYLE
Bi, L., Lu, X., Luo, J., Wang, K., & Zhang, Z. (2022). Hybrid dual attack on LWE with arbitrary secrets. Cybersecurity, 5(1). https://doi.org/10.1186/s42400-022-00115-y
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