Universal product learning with errors: A new variant of LWE for lattice-based cryptography

The middle product learning with errors problem (MP-LWE) is a variant of the learning with errors problem (LWE). The public-key cryptography under MP-LWE assumption gets an equilibrium between “efficiency” and “security”. However, the hardness of MP-LWE has not been sufficiently explored since its introduction. So in this paper, we focus on the hardness of MP-LWE.