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Performing TVLA test without knowledge of the Key

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https://www.rambus.com/wp-content/uploads/2015/08/TVLA-DTR-with-AES.pdf

As the paper shows, we can check the hardware if it is vulnerable to side channel attacks by performing this test, although is it possible to perform it even if the key is not known to us or it is known, but we cannot change the key? Do we have to adjust the test vectors by some linear operations, if the key is known?

Are there other methods that allow us to prove the hardware is vulnerable to side channel power analysis?

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