Post−quantum cryptography, as a key technology against possible threats from quantum computing, is now becoming the foundation of next−generation cryptographic systems. The global migration to PQC is underway, with many countries actively developing new standards. Among the various candidates, lattice−based cryptography algorithms are popular due to their efficiency and small key sizes. Security analysis is crucial for ensuring the reliability of PQC. This paper focuses on the security analysis of lattice−based cryptography. We first review the development of lattice attacks and their theoretical background. Then, we study the main memory bottleneck in the best current attack method, called sieving, especially when used at cryptographic scales. By improving both the algorithm and its implementation, we achieved some new record results. Our tests show that the previous view of memory efficiency as a critical factor in lattice cryptography security estimation is significantly flawed. Based on this, we provide recommendations for choosing parameters in PQC migration and deployment, especially for critical infrastructure like banking.