I Thought 128 Bits Was a Large Key Length

You may be accustomed to thinking of key size in terms of Blowfish, Triple DES (3DES), etc., in which a 128-bit key is considered strong. For symmetric encryption algorithms, in which a single shared key is used for both encryption and decryption, this is true. But in the world of public key cryptography, key sizes are larger by a factor of ten (roughly) due to the fact that public key crypto uses completely different math than symmetric crypto. In other words, it's an apples vs. oranges