Hybrid dual attack on LWE with arbitrary secrets

Abstract

Abstract 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.

Keywords

• Learning with errors
• Lattice-based cryptography
• Cryptanalysis
• Dual attack
• Hybrid attack
• NIST PQC