On Probability of Success in Linear and ... - Bilkent University

P(rank(k 0 ) ≤ r)
P(rank(k 0 ) ≤ r)
1
0.8
0.6
0.4
0.2
0
1
0.8
0.6
0.4
0.2
0
Equation (19), μ = 16
μ = 8
μ = 4
Experimental, μ = 16
μ = 8
μ = 4
5 10 15 20 25 30
r
(a) Attack on s-box 5; SN = 2.
Equation (19), μ = 12
μ = 6
μ = 2
Experimental, μ = 12
μ = 6
μ = 2
10 20 30 40 50
r
60 70 80 90 100
(b) Attack on s-boxes 2, 5, 6, 7, 8; SN = 2 16 .
Fig. 2. A comparison of equation (19) and the experimental success rates of the 6round
DES attacks tested. The results show a considerable difference for the lower
values of µ.
To trace the source of this error, we first looked into the normal approximation
for the binomial distribution. Recall that in formulation of the success
probability,
PS = P (T0 > W¯r)
=
� ∞ � x
0
−∞
fq(y) dy f0(x) dx . (23)
14