Cryptography Reference
In-Depth Information
x 10
−3
5.5
5
4.5
4
<−−−−Theoritical value (light)
3.5
<−−−−Experimental value (dark)
N=256
3
0
50
100
150
200
250
300
v −−−−>
FIGURE 3.5: Comparing experimental and theoretical values of P(S
N
[38] =
v) versus v.
lengths l (in bytes) along with the average ǫ and the maximum ǫ
max
of the
ǫ
u,v
's. u
max
and v
max
are the (u,v) values which correspond to ǫ
max
. Though
for some key lengths there are more than a hundred anomaly pairs, most of
them have ǫ
u,v
≤ 10%. To illustrate this, we look at the column n
10
which
shows how many of the anomaly pairs exceed the 10% error margin. The two
rightmost columns show what percentage of 256
2
= 65536 (total number of
(u,v) pairs) are the numbers n
5
and n
10
.
These results show that as the key length increases, the proportion of
anomaly pairs tends to decrease. With 256-byte key, there is no anomaly pair
with ǫ
u,v
> 5%, i.e., n
5
= 0. It has also been pointed out in [110] that as the
key length increases, the actual random behavior of the key is demonstrated
and that is why the number of anomaly pairs decrease and experimental results
match the theoretical formulae. In [110, Section 6.3.2] the anomalies are
discussed for rows and columns 9, 19 and also for the diagonal given short
keys as 5 bytes.
