International Association for Cryptologic Research

International Association
for Cryptologic Research


From MLWE to RLWE: A Differential Fault Attack on Randomized & Deterministic Dilithium

Mohamed ElGhamrawy , NXP Semiconductors, Hamburg, Germany; Hamburg University of Applied Sciences, Hamburg, Germany
Melissa Azouaoui , NXP Semiconductors, Hamburg, Germany
Olivier Bronchain , NXP Semiconductors, Leuven, Belgium
Joost Renes , NXP Semiconductors, Eindhoven, the Netherlands
Tobias Schneider , NXP Semiconductors, Gratkorn, Austria
Markus Schönauer , NXP Semiconductors, Gratkorn, Austria
Okan Seker , NXP Semiconductors, Hamburg, Germany
Christine van Vredendaal , NXP Semiconductors, Hamburg, Germany
DOI: 10.46586/tches.v2023.i4.262-286
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Abstract: The post-quantum digital signature scheme CRYSTALS-Dilithium has been recently selected by the NIST for standardization. Implementing CRYSTALSDilithium, and other post-quantum cryptography schemes, on embedded devices raises a new set of challenges, including ones related to performance in terms of speed and memory requirements, but also related to side-channel and fault injection attacks security. In this work, we investigated the latter and describe a differential fault attack on the randomized and deterministic versions of CRYSTALS-Dilithium. Notably, the attack requires a few instructions skips and is able to reduce the MLWE problem that Dilithium is based on to a smaller RLWE problem which can be practically solved with lattice reduction techniques. Accordingly, we demonstrated key recoveries using hints extracted on the secret keys from the same faulted signatures using the LWE with side-information framework introduced by Dachman-Soled et al. at CRYPTO’20. As a final contribution, we proposed algorithmic countermeasures against this attack and in particular showed that the second one can be parameterized to only induce a negligible overhead over the signature generation.
  title={From MLWE to RLWE: A Differential Fault Attack on Randomized & Deterministic Dilithium},
  journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
  publisher={Ruhr-Universität Bochum},
  volume={2023, Issue 4},
  author={Mohamed ElGhamrawy and Melissa Azouaoui and Olivier Bronchain and Joost Renes and Tobias Schneider and Markus Schönauer and Okan Seker and Christine van Vredendaal},