Cryptography Reference
In-Depth Information
Table 3.1
Number of faults to recover the 16th round key with a 99 % success rate
Round
Distinguisher
Bit error
Byte error
Chosen pos.
Random pos.
Chosen pos.
Random pos.
12
Likelihood
7
11
9
17
SEI
14
12
17
21
11
Likelihood
11
44
210
460
SEI
30
71
500
820
10
Likelihood
290
1500
13400
18500
SEI
940
2700
26400
23400
10
5
10
7
10
8
10
8
9
Likelihood
3
.
4
×
2
.
2
×
>
>
1
.
4
×
10
6
>
10
8
>
10
8
>
10
8
SEI
3.4.3 Attack Results
The results of several attack simulations are reported in [345]. The attacker is assumed
to be able to inject some fault in the left half of the DES internal state
L
r
at the end of
some round
r
. Several fault models are considered: either a single
bit is flipped or one byte is switched to a random value, and the fault position is
either random (among the 32 bit positions or the four byte positions in
L
r
) or chosen
by the attacker. In the latter case, the bit positions are chosen from among the ones
entering a single S-box in order to slow down the error propagation and maximize the
bias in the distribution of
∈{
9
,
10
,
11
,
12
}
L
15
while the byte positions are all chosen successively.
For every round number and every fault model, the likelihood distinguisher and the
SEI distinguisher are both applied. For the likelihood distinguisher, the distributions
(
Δ
p
i
(
·
))
i
have been empirically computed based on several correct and faulty encryp-
tions of random plaintexts under random keys.
3
Table
3.1
summarizes the numbers
of correct-faulty ciphertexts pairs required for a 99% success rate in recovering the
whole last round key.
The attacks on the 11th and 12th rounds are very efficient: less than 25 faults
are sufficient on the 12th round, while on the 11th round less than 100 faults are
sufficient in a bit error model and less than 1
10
3
faults are sufficient in a byte error
model. On the tenth round, the attacks are still fairly efficient: the best attack (chosen
position bit error model, likelihood distinguisher) requires 290 faults whereas the
least efficient attack (chosen position byte error model, SEI distinguisher) requires
2
×
10
4
faults. It is on round 9 that the attacks become quite costly since the most
efficient attack in the bit error model (chosen position, likelihood distinguisher)
requires around 3
.
64
×
10
5
.
4
×
faults and all the attacks in the byte error model require
more than 10
8
faults.
3
Note that the
(
p
i
(
·
))
i
distributions are almost independent of the secret key (this fact is argued in
[47]).
