Speed Advantage of Symmetric Key Encryption

We've all read that a symmetric or shared key i开发者_JAVA百科s faster than public-private keys. But what's the exact reason for this? It seems to me in either case encryption and decryption logic against a key of some kind must be performed.

Asymmetric encryption usually uses complex mathematical operations, such as power and modulus, on very large numbers (2048 bits). These operations take time.

Symmetric encryption uses simpler operations, such as XOR and multiply, on smaller numbers (64 or 128 bits). Hence they run faster.

Most systems use Asymmetric encryption to send a small key of 128 or 256 bits and then use that key to symmetrically encrypt/decrypt data files containing possibly megabytes of data.