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Revisiting the Robustness of (R/M)LWR under Polynomial Moduli with its Applications
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| Conference: | ASIACRYPT 2025 |
| Abstract: | This work conducts a comprehensive investigation on determining the entropic hardness of (Ring/Module) Learning with Rounding (LWR) under polynomial modulus. Particularly, we establish the hardness of (M)LWR for general entropic secret distributions from (Module) LWE assumptions based on a new conceptually simple framework called rounding lossiness. By combining this hardness result and a trapdoor inversion algorithm with asymptotically the most compact parameters, we obtain a compact lossy trapdoor function (LTF) with improved efficiency. Extending our LTF with other techniques, we can derive a compact all-but-many LTF and PKE scheme against selective opening and chosen ciphertext attacks, solely based on (Module) LWE assumptions within a polynomial modulus. Additionally, we show a search-to-decision reduction for RLWR with Gaussian secrets from a new Rényi divergence-based analysis. |
BibTeX
@inproceedings{asiacrypt-2025-35964,
title={Revisiting the Robustness of (R/M)LWR under Polynomial Moduli with its Applications},
publisher={Springer-Verlag},
author={Haoxiang Jin and Feng-Hao Liu and Zhedong Wang and Yang Yu},
year=2025
}