Cryptography has evolved from simple ciphers to advanced systems securing information against eavesdropping and tampering. Modern cryptography uses symmetric keys or public-private key pairs for encryption and decryption. Public key cryptography, like RSA and elliptic curve cryptography, relies on hard mathematical problems for security. However, quantum computing poses a threat to these systems. To counter this, NIST has standardized quantum-resistant algorithms, including CRYSTALS-Kyber and FALCON, etc. Inspired by FALCON, the internationally-developed SOLMAE in Korea improves efficiency by simplifying key processes while maintaining security. This monograph explores FALCON and SOLMAE’s procedures, focusing on their implementation, verification by Python script, and future challenges.