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Rounding in the Rings

Authors:
Feng-Hao Liu , Florida Atlantic University
Zhedong Wang , Florida Atlantic University
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DOI: 10.1007/978-3-030-56880-1_11 (login may be required)
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Conference: CRYPTO 2020
Abstract: In this work, we conduct a comprehensive study on establishing hardness reductions for (Module) Learning with Rounding over rings (RLWR). Towards this, we present an algebraic framework of LWR, inspired by a recent work of Peikert and Pepin (TCC '19). Then we show a search-to-decision reduction for Ring-LWR, generalizing a result in the plain LWR setting by Bogdanov et al. (TCC '15). Finally, we show a reduction from Ring-LWE to Module Ring-LWR (even for leaky secrets), generalizing the plain LWE to LWR reduction by Alwen et al. (Crypto '13). One of our central techniques is a new ring leftover hash lemma, which might be of independent interests.
Video from CRYPTO 2020
BibTeX
@inproceedings{crypto-2020-30370,
  title={Rounding in the Rings},
  publisher={Springer-Verlag},
  doi={10.1007/978-3-030-56880-1_11},
  author={Feng-Hao Liu and Zhedong Wang},
  year=2020
}