Cryptography Reference
In-Depth Information
GF(2
33
)
.
for K
∈
Prove that
DP
max
=
LP
max
=
2
−
32
.
Deduce that for any K we have
DP
F
max
≤
2
−
31
and
LP
F
max
≤
2
−
31
.
Deduce that for a Feistel cipher with at least three rounds with the above round
function, we have
EDP
max
≤
2
−
61
. (This is used in order to con-
struct the PURE cipher which was invented by Kaisa Nyberg and Lars Knudsen.)
9
2
−
61
and
ELP
max
≤
m
be a random permutation. We compare C to
a uniformly distributed permutation. Show that
m
Exercise 4.4.
Let C
:
{
0
,
1
}
→{
0
,
1
}
1. the property
Dec
d
(
C
)
=
0
does not depend on the choice of the distance on the
matrix space,
2. if
Dec
1
(
C
)
0
, then the cipher C provides perfect secrecy for any distribution
of the plaintext,
3. if
Dec
2
(
C
)
=
=
0
, then C is a Markov cipher.
m
be a random permutation. We compare C to a
uniformly distributed permutation. We consider decorrelation defined by the adaptive
norm
(
m
Exercise 4.5.
Let C
:
{
0
,
1
}
→{
0
,
1
}
||
.
||
a
)
.
1. Prove that
Dec
d
−
1
(
C
)
Dec
d
(
C
)
.
≤
Dec
d
(
C
)
2. Prove that
0
≤
≤
2
.
C
∗
:
m
m
be random permutations. We assume that
Exercise 4.6.
Let C
,
{
0
,
1
}
→{
0
,
1
}
C
∗
is uniformly distributed. Show that
ε
,
C
∗
)
≤
ε
1. C is
-strongly universal implies
2BestAdv
Cl
a
(
C
,
-strongly universal implies
EDP
max
≤
ε
2. C is
ε
,
-XOR universal implies
EDP
max
≤
ε
ε
3. C is
.
Exercise 4.7.
Let f
K
:
{
0
,
1
}
m
→{
0
,
1
}
m
be a function defined by a random key K in
a key space
K
. We compare f
K
to a uniformly distributed function.
1. Prove that if
Dec
d
(
f
K
)
2
md
.
=
0
, then
#
K
≥
K , we obtain
Dec
1
(
f
K
)
2. Show that for f
K
(
x
)
=
x
⊕
=
0
.
3. Propose a construction for f
K
such that
Dec
d
(
f
K
)
2
md
.
=
0
and
#
K
=
m
2
Exercise 4.8.
Prove that for any independent random function F
1
,...,
F
r
on
{
0
,
1
}
such that
F
∗
)
BestAdv
Cl
a
(
F
i
,
≤
ε
9
This exercise was inspired by Ref. [141].
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