Cryptology ePrint Archive: Report 2020/292

LWE with Side Information: Attacks and Concrete Security Estimation

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

Abstract: 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.

Category / Keywords: public-key cryptography / LWE, NTRU, Lattice reduction, Cryptanalysis, Side-channels analysis, decryption failures.

Date: received 5 Mar 2020, last revised 29 Jul 2020

Contact author: danadach at ece umd edu,l ducas@cwi nl,gong@cs umd edu,melissa rossi@ens fr

Available format(s): PDF | BibTeX Citation

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.

Version: 20200729:101116 (All versions of this report)

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