On the hardness of the Module Learning With Errors problem

The Module Learning With Errors (M-LWE) problem 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 talk, I will present recent results on the theoretical hardness of M-LWE.

Based on joint works with Katharina Boudgoust, Corentin Jeudy, and Weiqiang Wen.