You need both constant power hardware and software to be immune (and to related timing attacks). The libsecp256k1 library for example is designed to be timing a

You need both constant power hardware and software to be immune (and to related timing attacks). The libsecp256k1 library for example is designed to be timing attack resistant, but I'm still working on verifying how power sidechannel resistant it is. Using an internal power source, like a primary lithium cell, is one way to circumvent the power sidechannel. But power sidechannels can also easily become RF sidechannels, so it's still good to minimize them.