Cryptography Reference
In-Depth Information
Table 2.
The first column consists of numbers from [7]. The entries in the columns
plaintext, key, plaintext and key show the best collision attacks for the modes when
there is difference only in the plaintext, only in the key or both in the plaintext and key,
respectively. The abbreviations C, PC, SFSC, FSC stand for collision, pseudo-collision,
semi-free start collision, free start collision, respectively.
mode
(
ı
)
plaintext
and key
h
plaintext
key
PC
a
1
E
h
(
m
)
⊕ m
C, SFSC
FSC
2
E
h
(
h ⊕ m
)
⊕ h ⊕ m
C, SFSC
PC
PC, FSC
3
E
h
(
m
)
⊕ h ⊕ m
C, SFSC
PC
FSC
4
E
h
(
h ⊕ m
)
⊕ m
C, SFSC
PC
PC, FSC
C
a
,SFSC
a
5
E
m
(
h
)
⊕ h
PC
FSC
6
E
m
(
h ⊕ m
)
⊕ h ⊕ m
PC
FSC
C, SFSC, FSC
7
E
m
(
h
)
⊕ h ⊕ m
PC
C, SFSC
FSC
8
E
m
(
h ⊕ m
)
⊕ h
PC
FSC
C, SFSC, FSC
PC
a
9
E
h⊕m
(
m
)
⊕ m
FSC
C, SFSC, FSC
C
a
,SFSC
a
10
E
h⊕m
(
h
)
⊕ h
FSC
PC, FSC
E
h⊕m
(
m
)
⊕ h
11
FSC
PC
C, SFSC, FSC
12
E
h⊕m
(
h
)
⊕ m
FSC
C, SFSC
C, PC, FSC
a
When key collisions exist in the cipher.
Table 3.
In the first column A-DM, T-DM, DBL and MDC-2 are abbreviations of
Abrest DM, Tandem DM, Double-Block-Length and Modification Detection Code 2
respectively (see [20] for the first two, [14] for the third and [8] for the last). The
abbreviations C, PC, SFSC, FSC stand for collision, pseudo-collision, semi-free start
collision, free start collision, respectively.
plaintext
and key
(
h
,g
)
mode
plaintext
key
h
=
E
g,m
(
h
)
⊕ h
g
=
E
m,h
(
g
)
⊕ g
A-DM
FSC
C, SFSC
PC, FSC
h
=
E
g,m
(
h
)
⊕ h
g
=
E
m,E
g,m
(
h
)
(
g
)
⊕ g
T-DM
FSC
C, SFSC
PC, FSC
h
=
E
hm
(
g ⊕ c
)
⊕ g ⊕ c
g
=
E
hm
(
g
)
⊕ g
DBL
PC
C, PC, SFSC, FSC PC, FSC
MDC-2
h
=(
E
h
(
m
)
⊕ m
)
L
(
E
g
(
m
)
⊕ m
)
R
g
=(
E
g
(
m
)
PC
a
C, SFSC
FSC
⊕ m
)
L
⊕ m
)
R
(
E
h
(
m
)
a
When key collisions exist in the cipher.
Although we have analyzed the collision resistance of the above modes, the
differential trails for the underlying ciphers in the open-key model can be used
as a standalone cryptanalytical result for the compression functions.
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