Cryptography Reference
In-Depth Information
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Reference
Hamming
Residue Mod 7
Parity
Double Parity
Complementary Parity
Residue Mod 3
0.2
0.1
0
0
5
10
15
20
25
30
35
40
45
50
Number of Traces
Fig. 15.9
Success rate of the correlation-based DPA attack versus the number of traces using attack
hypothesis of the full size of the output register (the adversary is aware of the error detection and
correction code used)
all the 256 possible keys and randomly selecting the input plaintext. For the first
set of experiments, the correlation between the Hamming weight of the eight-bit
S-box output and the power traces was calculated for all the considered circuits. The
underlying assumption was that the adversary is unaware of the presence of the error
detection/correction circuit and can therefore construct only an approximated power
model. In the second set of experiments we computed the correlation between the
power traces and the Hamming weight of the full output of the S-box (including the
check bits), thus assuming that the attacker is aware of the particular redundancy
added to the S-box circuit.
Using the results of all the attacks that were mounted, we can compute the first
order success rate [384], defined below. Given an adversary who attacks a secret key
K
and generates
n
key guesses
g
that are sorted according to the
attack result (correlation-based DPA in our case), we define a function
f
that returns
1 if the correct key is
g
1
and 0 otherwise. The first-order success rate of the attack
against the secret key
K
is defined as
=[
g
1
,
g
2
,...,
g
n
]
Succ
attack
=
[
=
]
.
Pr
f
1
(15.2)
We concentrate on one of the intermediate situations discussed in Sect.
15.4.3
,
where the noise is present but is not sufficiently high to completely overshadow the
signal and cause the attack to fail. To simulate the noise conditions, we added white
noise to the traces generated by the transistor-level simulator.
Figures
15.9
and
15.10
show the success rate of the correlation-based DPA as a
function of the number of traces for a fixed value of the noise standard deviation
(equal to 5
10
−
4
) using two different attack hypotheses. Figure
15.9
shows the
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