Is it possible for an adversary to gain knowledge of the secret key by analyzing the power consumption of an AES hardware core? I think he/she can't, but I am having difficulty to give a reasonable explanation.
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There are many ways to attempt to infer information about cryptographic operations, anything from processing time (see: hardware optimization analysis) to unintended emssisions (https://en.wikipedia.org/wiki/Van_Eck_phreaking but on the processor itself) to as you asked: Differential Power Analysis (https://people.rit.edu/kjm5923/DPA_attacks_on_AES.pdf)
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1So the brief answer is: "yes" :-). – sleske Jul 10 '17 at 08:34
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1It depends on the implementation. This is a type of side channel attack. On well implemented cryptographic system, this should be very difficult if not impossible to infer keys based on energy usage or timing or emission, but it is difficult to ascertain that a system doesn't have any side channel vulnerability. – Lie Ryan Jul 19 '17 at 11:56