Error analysis of weak Poly-LWE instances

Abstract

Error distribution plays a central role in the security of encryption based on the Learning with Errors (LWE) problem and its variants. In this paper, we investigate the error distribution of weak Poly-LWE instances. For this purpose, we derive a closed-form formula to compute the mapped error distribution. With this algebraic approach to evaluate the error, we examine the recently proposed attacks on Poly-LWE and Ring-LWE and reassess their parameters in order to include more instances. Notably, our method can also be applied to non-Gaussian error. We conduct experiments to investigate the shape of the mapped error distribution and confirm that in many cases it is no longer Gaussian nor uniform; our experimental results from distinguishers also validate our theoretical analysis.