Earlier quoted context omitted.
No algorithm is secure by design against these DPA attacks. They exploit data-dependencies. The only 'provably secure' (e.g., on paper (+)) countermeasure you can apply to these symmetric schemes is something typically called masking. You can view masking as using secret sharing techniques to split up all intermediate computation into independent operations. To defeat masking an attacker needs to be able to re-combin…
How about a "security through obscurity" countermeasure for sensitive systems where we'd use a special compiler that adds a bunch of "noise" in the generated algorithm (useless instructions etc...)? Or alternatively run the algorithm through an emulator that does the same thing.
However, the attacks all rely on reducing noise by combining measurements. Introducing sufficiently-long random delays or sufficiently-big variations in clock speed can make it harder to combine measurements, and can thus stop such attacks. Unfortunately, making trace alignment hard is not so much a provably-correct fix as a contest between the hardware designer's ability to be really annoying and the attacker's intuition (to find usable synchronization points) and sheer persistence.
(If you want to rely on such things, you really need to get a top-notch hardware attack lab such as Riscure to look at your countermeasures; you really want to test against an experienced attacker's intuition.)