From: jel@sutro.SFSU.EDU (John E. Levine)
Date: Tue, 30 Nov 93 19:57:52 PST
To: cypherpunks@toad.com
Subject: soundfile stego
Message-ID: <9312010353.AA00175@russian.SFSU.EDU>
MIME-Version: 1.0
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You know, you don't have to think of somehow modifying
a file pointwise in the time domain.  How about this,
to stego a sound file:

Do an FFT of the *entire* file.  Assuming the file
is two hours = 7200 seconds, the frequency res of
the transformed file will be about 140 microhertz.
Pick a band that humans don't usually pay much
conscious attention to when they hear music; say 18
KHz through 19.5 KHz.  Replace the low bit in each
of these frequency space samples (there are 1500 /
0.000140 ~= 1E7 such samples) with the stego data.
Inverse transform the modified, frequency space
representation of the file back into the time domain,
and voila! I suspect you would not be able to tell the
difference from the original with your naked ears.
But this is not repudiable; I suspect the spectrum
of the file would look artificial.

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Also, I am told that humans have a tough time identifying
the phase of the frequency components of the sounds they
identify.  So one could hide date in the phase relationships
among the frequency components of, say, recorded speech.