Welcome to the resource topic for
**2022/472**

**Title:**

On the Hardness of Module Learning With Errors with Short Distributions

**Authors:**
Katharina Boudgoust, Corentin Jeudy, Adeline Roux-Langlois, Weiqiang Wen

**Abstract:**

The Module Learning With Errors problem (M-LWE) is a core computational assumption of lattice-based cryptography which offers an interesting trade-off between guaranteed security and concrete efficiency. The problem is parameterized by a secret distribution as well as an error distribution. There is a gap between the choices of those distributions for theoretical hardness results (standard formulation of M-LWE, i.e., uniform secret modulo q and Gaussian error) and practical schemes (small bounded secret and error). In this work, we make progress towards narrowing this gap. More precisely, we prove that M-LWE with \eta-bounded secret for any 2 \leq \eta \ll q and Gaussian error, in both its search and decision variants, is at least as hard as the standard formulation of M-LWE, provided that the module rank d is at least logarithmic in the ring degree n. We also prove that the search version of M-LWE with large uniform secret and uniform \eta-bounded error is at least as hard as the standard M-LWE problem, if the number of samples m is close to the module rank d and with further restrictions on \eta. The latter result can be extended to provide the hardness of M-LWE with uniform \eta-bounded secret and error under specific parameter conditions.

**ePrint:**
https://eprint.iacr.org/2022/472

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

**Example resources include:**
implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .