I think the goal is not necessarily constant time, but more like do the same things independently from the bits of the secrets (symmetric keys, private keys, et

I think the goal is not necessarily constant time, but more like do the same things independently from the bits of the secrets (symmetric keys, private keys, etc.). As a result, you get constant time. But you get much more, because if one analyzes physical conditions (cpu/memory usage, temperature, time itself), he can't gather information about the secrets.