This attack has been successfully implemented against smart cards and other security tokens, and against electronic commerce servers across the Internet. The effects of this attack can be devastating. The first is as a chunk of math. Traditionally, cryptanalysis has been directed solely against the math. On the other hand, timing attacks, power analysis, and fault analysis all makes assumptions about implementation, and uses additional information garnered from attacking those implementations.
Timing attacks assumes that an attacker knows how long a particular encryption operation takes.
I like to think of these attacks as biological. There are some things you just can't learn about an organism by taking it apart. Sometimes you have to look at the inputs and outputs. Call them side-channel attacks. Normal attacks look at the plaintext and the ciphertext and attempt to recover the key.