The polynomial learning with errors problem and the smearing condition

Abstract As quantum computing advances rapidly, guaranteeing the security of cryptographic protocols resistant to attacks is paramount. Some leading candidate cryptosystems use learning with errors (LWE) problem, attractive for its simplicity and hardness guaranteed by reductions from hard computational lattice problems. Its algebraic variants, ring-learning (RLWE) polynomial (PLWE), gain efficiency over standard LWE, but their remains be thoroughly investigated. In this work, we consider “smearing” condition, a condition on PLWE RLWE introduced in Elias et al. We expand upon some questions about smearing posed show how related coupon collector’s problem. Furthermore, develop an algorithm probabilities smearing. Finally, present smearing-based solving