Core Encryption Methods in hardware wallets utilize advanced cryptographic algorithms such as AES (Advanced Encryption Standard), RSA (Rivest-Shamir-Adleman), and ECC (Elliptic Curve Cryptography) to ensure the security of private keys. These methods are essential for protecting sensitive information from unauthorized access and attacks. By employing these encryption techniques, hardware wallets can securely store private keys offline, making them less vulnerable to hacking attempts that target online wallets. This feature is crucial for users who prioritize security in their cryptocurrency transactions and holdings.