That is very interesting! I worked on a similar idea (but on the malware side… :-p) a few years back. The idea of our paper [1] is that if programs could run and at the same time produce a functionally equivalent to themselves program that uses different instructions (to do the same thing), then power fingerprinting these programs would be very hard, as each execution's power trace would be different. We implemented…
Wow, you seem to have been way ahead of this project! It seems like this is a kind of equivalent to constant-time operations -- but constant-power operations? Is that also relevant to defending against DPA? Should we think of the proposed technique as a new application of DPA? (Is Cryptography Research going to sue them?)
Not really, like I said the idea is similar but as fabulist pointed out [1], they have a whitelist approach so I'm not really sure that our idea could systematically break their system.
> It seems like this is a kind of equivalent to constant-time operations -- but constant-power operations?
You get the right intuition, but no. There are constant-power countermeasures but this is not it. You see, there are two types of side-channel countermeasures: palliatives and curatives. Palliative countermeasures, like the one we discussed in the paper I mentioned in my previous comment, attempt to make the attack more difficult by blurring the information the attacker has access to using randomness, but there is no theoretical foundation behind. By contrast, curative countermeasures aim at providing a leak-free implementation based on a security rationale. There are two strategies to achieve this: the first one is to make the leakage as decorrelated as possible from the sensitive data (masking), and the second one is to make the leakage constant, irrespective of the sensitive data (balancing).
So your idea of constant-power exists, it is called balancing. I worked on this kind of countermeasures at assembly code level [2] if you are interested, and there are many other very interesting papers in the references to go through.
> Is that also relevant to defending against DPA?
Yes, it is mostly relevant against DPA. Actually constant-power operations are good against DPA, but absolutely not against PFP (what the linked post describes) since it makes it easier: it's always the same power trace!
> Should we think of the proposed technique as a new application of DPA? (Is Cryptography Research going to sue them?)
Since it seems to be done live I would rather say SPA (Simple Power Analysis) than DPA, but I guess the safer is to say that it is a (possibly new) application of the power side channel analysis.
(I don't know.)