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.
CITATION STYLE
Liu, F. H., & Wang, Z. (2020). Rounding in the rings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12171 LNCS, pp. 296–326). Springer. https://doi.org/10.1007/978-3-030-56880-1_11
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