Cryptography Reference
In-Depth Information
1
2
3
⊕
⊕
⊕
P
i
P
i
+1
P
i
+2
K
K
K
D
D
D
C
i
C
i
+1
C
i
+2
4
Figure 4.13.
Effect of a 1-bit transmission error using CBC mode
and is therefore correct, since
C
i
−
1
was received correctly. However, when the
incorrect contents of the bottom register are added to the correct contents of
the top register, the resulting plaintext block
P
i
is incorrect.
2. The incorrect
C
i
is now put into the top register. When the next correct
ciphertext block
C
i
+
1
is received, it is decrypted, resulting in a correct value
being placed in the bottom register. However, the contents of the top register
remain incorrect. When the correct contents of the bottom register are added
to the incorrect contents of the top register, the resulting plaintext block
P
i
+
1
is
incorrect.
3. The correct
C
i
+
1
is now put into the top register. When the next correct
ciphertext block
C
i
+
2
is received, it is decrypted and the correct value is placed
in the bottom register. The contents of the top register are now also correct
and so the addition of the contents of the top and bottom registers results in a
correct plaintext block
P
i
+
2
.
4. The error has now worked its way out of the system and assuming that
subsequent ciphertext blocks do not contain transmission errors, the remaining
plaintext blocks will be recovered correctly. We thus see that in a similar manner
to CFB mode, although a 1-bit error in the ciphertext propagates to affect two
blocks of plaintext, the process quickly recovers.
The extent to which these two plaintext blocks are incorrect can be established in
a similar way to that of CFBmode. In fact the impact is the same as for CFBmode,
except in the reverse order. In other words, the first incorrect plaintext block
P
i
is
'very wrong' (about half of its bits are incorrect) but the second incorrect plaintext
block
P
i
+
1
is only incorrect in the same bit position that
C
i
is incorrect. Just as for
CFB mode, CBC mode has recovered remarkably well from a 1-bit transmission
error.
