Databases Reference
In-Depth Information
False detection rates
The sensitivity of a watermarking scheme can be measured by the following
false detection rates in watermark detection.
•
For robust watermarking, we have
-
False hit
: the probability of the original watermark being detected from
unmarked data or a fictitious watermark being detected from water-
marked data (i.e., invertibility attack).
-
False miss
: the probability of not detecting the original watermark from
watermarked data.
•
For fragile watermarking, we have
-
False hit
: the probability of the original watermark being detected from
unmarked data.
-
False miss
: the probability of not detecting any change to the embedded
watermark from watermarked data.
The false detection rates in watermark detection must be low enough (e.g.,
10
−
9
) in order for the detection result to be used as proof in court. The
false miss rate should be investigated in the presence of various database
attacks. Since the fragile watermark is not used for copyright protection, the
invertibility attack is not meaningful.
4.1 Robust Watermarking
The robustness of watermarking can be achieved by using majority vote
in watermark detection, as in Agrawal and Kiernan's scheme, or using ECC
code, as in Sion's scheme. For simplicity reasons, we focus on Agrawal and
Kiernan's scheme.
Consider Bernoulli trials with probability
p
of success and
q
of failure.
Let
b
(
k
;
m, p
)=
k
p
k
q
m−k
be the probability that
m
Bernoulli trials result
k
failures, where
k
=
m
!
in
k
successes and
m
m
.Let
B
(
k
;
m, p
)=
i
=
k
+1
b
(
i
;
m, p
) be the probability of having
more than k
suc-
cesses in
m
Bernoulli trials. In Agrawal and Kiernan's scheme, a watermark
is detected if more than
τ
in percentage of the embedded bits are detected
correctly. If the watermark detection is applied to unmarked data (or water-
marked data with a different secret key), the detection can be considered as
Bernoulli trials with a probability of 1
/
2 that a correct value will be found in
a specific bit position. Assuming
ω
bits are checked in watermark detection,
then the false hit rate is
B
(
−
k
!(
m−k
)!
,
0
≤
k
≤
;
ω,
0
.
5). The false hit rate is extremely low if
τ
and
ω
are reasonably large. For example, the false hit rate can be as low as
10
−
10
for
τ
τω
1000.
The false miss rate can be analyzed under various attack scenarios. A
typical modification attack is that an attacker randomly flips every least sig-
nificant bit with a probability
p<
0
.
5 (if
p
≥
0
.
6and
ω
≥
0
.
5, one can flip every bit back
before watermark detection). For the detection algorithm to fail to recover the
≥
