Mitigating Side Channel Attack (SCA) The SCA power attack described in 2016 article called "Power Side Channels in Security ICs: Hardware Countermeasures", depends on the measurement of power consumption fluctuations during AES-128 execution, for either known plain text, or known cipher text. In addition, the attacker has the ability to change the cipher text (CPA attack). Nevertheless only one of them, either the plain text or the cipher text need to be known to the attacker.

Suppose one avoids exposing both of them, for instance by using secret internal key AND secret internal counter for counter (CTR) mode encryption. In that case the AES-128 block cipher encrypts a counter that is not known with a key that is not known.

Additionally the cipher text is located in an external Flash. And finally, the attacker cannot change the cipher text, as described in the article.

Is such a scheme still exposed to side channel attacks?
As you are always decrypting the same flash content with the same key, statistical attacks like DPA do not work, as they try to find dependencies between two random variables (one being an intermediate value predicted using parts of the key and the other one being the measured current consumption(s)), where in your case one of them is constant.

The only uses an attacker can get from several measurements (instead of using just one) is to take the average to reduce the noise or to apply an attack that exploits the noise. Otherwise the attacker basically has to use an attack that works with a single power trace.

If an attacker is able to run the identical software on an identical device where (s)he can choose the key and the cipher text, (s)he can use it to run the profiling phase for a template attack, and hope that both devices have very similar power characteristics.

As template attacks calculate likelihoods depending on the observed noise, you can combine the results of several measurements to improve your chances to recover key and data.

From my experience the success probability for a very skilled attacker (using an optimal template attack implementation combined with key enumeration techniques) are relatively low if the AES is implemented in hardware, but pretty good for a software implementation on a leaky device.