  As quantum computing advances rapidly, guaranteeing the security of
cryptographic protocols resistant to quantum attacks is paramount. Some leading
candidate cryptosystems use the Learning with Errors (LWE) problem, attractive
for its simplicity and hardness guaranteed by reductions from hard
computational lattice problems. Its algebraic variants, Ring-Learning with
Errors (RLWE) and Polynomial Learning with Errors (PLWE), gain in efficiency
over standard LWE, but their security remains to be thoroughly investigated. In
this work, we consider the "smearing" condition, a condition for attacks on
PLWE and RLWE introduced in [6]. We expand upon some questions about smearing
posed by Elias et al. in [6] and show how smearing is related to the Coupon
Collector's Problem Furthermore, we develop some practical algorithms for
calculating probabilities related to smearing. Finally, we present a
smearing-based attack on PLWE, and demonstrate its effectiveness.
