Cryptography Reference
In-Depth Information
Synchronization can also be automatically detected by attempt-
ing to extract the message. Imagine that the receiver knows that a
hidden message has been encoded in a sound file but doesn't know
where the message begins or ends. Finding the correct offset is not
hard with a guided search.
The message might include a number of parity bits, and a basic
error-detecting solution. That is, after every eight bits, an extra parity
Chapter 3 discusses
error-detecting and
error-correcting codes.
bit is added to the stream based on the number of 1s and 0s in the
previous eight bits. It might be set to 1 if there's an odd number and 0
if there's an even number. This basic error detection protocol is used
frequently in telecommunications.
This mechanism can also be used to synchronize the message
and find the location of the starts of the blocks through a brute-force
search. The file can be decoded using a variety of potential offsets.
The best solution will be the one with the greatest number of correct
parity bits. The search can bemade a bitmore intelligent because the
quality of the message is close to a continuous function. Changing
the offset a small amount should only change the number of correct
parity bits by a correspondingly small amount.
Many attacks like the
StirMark tests destroy
the synchronization.
Chapter 13 discusses
one way to defend
against it.
More sophisticated error-correcting codes can also be used. The
best offset is the one that requires the fewest number of corrections
to the bit stream. The only problem with this is that more correcting
power requires more bits, and this means trying more potential off-
sets. If there are 12 bits per word and 1000 samples encoding each
bit, then the search for the correct offset must try all values between
0
and
12000
.
14.3.3 Strengthening the System
Spreading the information across multiple samples can be strength-
ened by using another source of randomness to change the way that
data is added or subtracted from the file. Let
α
i
be a collection of co-
efficients that modify the way that the sum is calculated and the sig-
nal is extracted. Instead of computing the basic sum, calculate the
sum weighted by the coefficients:
α
i
x
i
.
can act like a key if they are produced by a crypto-
graphically-secure random number source. One approach is to use
a random bit stream to produce values of
The values of
α
1
.
Only someone with the same access to the random number source
can compute the correct sum and extract the message.
α
equal to either
+1
or
−
