How do public and private keys interact mathematically?
Data encrypted with a public key can only be decrypted by its corresponding private key. Conversely, a digital signature created with a private key can be verified by anyone holding the matching public key.
Why is asymmetric encryption rarely used to encrypt large files directly?
Asymmetric operations are computationally expensive (thousands of times slower than symmetric ciphers). In practice, hybrid encryption is used: an asymmetric cipher encrypts a fast symmetric session key (like AES-256), which encrypts the file.