Cryptography Reference
In-Depth Information
15.4 Echo Hiding
Hiding information in the noise of sound files is a good solution,
but the information may be erased by good compression algorithms.
Daniel Gruhl, Anthony Lu, and Walter Bender suggest tweaking the
basic acousitics of the room to hide information. While this can still
be obscured by sufficiently strong compression, it is oftenmore likely
to withstand standard algorithms. Echoes are part of recordings and
sophisticated listeners with trained ears can detect small changes in
them. Good recording engineers and their compressionists try to
avoid eliminating the echos in an effort to provide as much verisimil-
itude as possible.[GLB96]
Many recording software programs already include the ability to
add (or subtract) echoes from a recording. They can also change the
character of the echo by twiddling with strength of the echo and the
speed at which it vanishes.
Information can be included by changing either the strength or
the length of the decay. Gruhl, Lu and Bender report success with
encoding a single bit by changing the length of time before the echo
begins. A one gets a short wait (about .001 seconds) and a zero gets
a slightly longer wait (about .0013 seconds). More than one bit is en-
coded by splitting up the signal and encoding one bit in each seg-
ment.
The signal is detected by autocorrelation. If the audio signal is
represented by
f
(
t
)
, then the bit is extracted by computing
f
(
t
+
.
001)
and
0013)
. Segments carrying a signal of one will generally
produce a higher value of
f
(
t
+
.
001)
and segments carrying a signal
of zero will produce a higher value of
f
(
t
+
.
0013)
.
The bandwidth available depends on the sampling rate and a
lesser amount on the audio file itself. Higher-frequency sounds and
higher sampling rates can provide accurate results with shorter seg-
ments, both alone and in combination. Gruhl, Lu and Bender report
success with segments lasting one-sixteenth of a second.
The success of this algorithm depends, to a large extent, on the
ears listening to it. Some humans are born with good hearing, some
train their ears to hear better, and some do both. The music indus-
try continues to experiment with techniques like echo hiding to add
a watermark to recordings. The results are often quite good, but still
problematic. In many cases, the average human can't detect the ad-
ditional echo. Many of those who do detect it think the sound is
richer. Still, some of the best artists in the business often reject any
change to their perfect sound. At times, this debate can ring with
irony. Garage bands devoted to making noisy, feedback-rich music
f
(
t
+
.
