![](bg6.png)
Figure 4: Difference for a correct guess on k
i+1
⊕ k
i
.
Figure 5: Difference for a wrong guess on k
i+1
⊕ k
i
.
In Fig. 4 and Fig. 5 we provide the ADPA obtained
for an RSA of size 1024 bits and using 4000 traces.
We can see the peak in Fig. 5 showing that the guess
g is not correct. There is no peak in Fig. 4 which
means that the guess is correct.
This experimentation shows that the proposed ap-
proach is effective to extract the whole key. This
means that Algorithm 3 does not provide the claimed
protection from ADPA. This attack works even if the
elements are blinded at the beginning of the expo-
nentiation, by either a randomized representation or
a multiplication with a random element.
5 CONCLUSION
In this paper we considered two exponentiation al-
gorithms (Algorithm 2 and 3) proposed in (Tunstall
et al., 2018) with randomized store and load in or-
der to counter-act address bit differential power anal-
ysis. We analyzed the security of these approaches,
and we showed that Algorithm 3 has a an important
flaw. Indeed, the operation done in Step 3 of Algo-
rithm 3 is a square or multiplication depending on
the bit used for load and store randomization. With
a simulated power consumption we showed that we
can distinguish a square from a multiplication. This
means that the randomization of loads and stores in
Algorithm 3 is not effective anymore and an ADPA
can be conducted to recover the whole secret key with
a few thousand power traces.
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