In [1] P. Kocher et al. introduced Differential Power Analysis (DPA), a statistical test (the difference of means) to retrieve secret keys from smart cards power consumption. For the correct hypothesis on the key, the difference of means is significantly different from zero. Hence a large peak is observed in the trace of the difference of means for the correct hypothesis. In the first part of this paper we explain why even with an arbitrarily large number of experiments, the difference of means is not always null for incorrect hypotheses on the key. We show further that peaks observed in the traces of the difference of means for incorrect hypotheses are inherent to the attacked algorithm and that this knowledge can be used to enhance power analysis attacks. Finally we propose another test that under some conditions efficiently detects the correct hypothesis even if incorrect hypotheses show larger peaks on the curves representing the difference of means. The combination of these methods can reduce the number of messages necessary to retrieve a key from a device by a factor greater than 2.
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