Paper 2020/292

LWE with Side Information: Attacks and Concrete Security Estimation

Dana Dachman-Soled, Léo Ducas, Huijing Gong, and Mélissa Rossi


We propose a framework for cryptanalysis of lattice-based schemes, when side information---in the form of ``hints''--- about the secret and/or error is available. Our framework generalizes the so-called primal lattice reduction attack, and allows the progressive integration of hints before running a final lattice reduction step. Our techniques for integrating hints include sparsifying the lattice, projecting onto and intersecting with hyperplanes, and/or altering the distribution of the secret vector. Our main contribution is to propose a toolbox and a methodology to integrate such hints into lattice reduction attacks and to predict the performance of those lattice attacks with side information. While initially designed for side-channel information, our framework can also be used in other cases: exploiting decryption failures, or simply exploiting constraints imposed by certain schemes (LAC, Round5, NTRU). We implement a Sage 9.0 toolkit to actually mount such attacks with hints when computationally feasible, and to predict their performances on larger instances. We provide several end-to-end application examples, such as an improvement of a single trace attack on Frodo by Bos et al (SAC 2018). In particular, our work can estimates security loss even given very little side information, leading to a smooth measurement/computation trade-off for side-channel attacks.

Note: Revision note: - Improved use of side-channel information in Section 6.1. - Further remarks regarding symmetries for the case of NTRU in section 6.3.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
LWENTRULattice reductionCryptanalysisSide-channels analysisdecryption failures.
Contact author(s)
danadach @ ece umd edu
l ducas @ cwi nl
gong @ cs umd edu
melissa rossi @ ens fr
2020-07-29: last of 2 revisions
2020-03-06: received
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      author = {Dana Dachman-Soled and Léo Ducas and Huijing Gong and Mélissa Rossi},
      title = {LWE with Side Information: Attacks and Concrete Security Estimation},
      howpublished = {Cryptology ePrint Archive, Paper 2020/292},
      year = {2020},
      note = {\url{}},
      url = {}
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