From: Timothy Newsham <newsham@wiliki.eng.hawaii.edu>
Date: Tue, 30 Nov 93 22:32:18 PST
To: jel@sutro.SFSU.EDU (John E. Levine)
Subject: Re: soundfile stego
In-Reply-To: <9312010353.AA00175@russian.SFSU.EDU>
Message-ID: <9312010631.AA22105@toad.com>
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.

The FFT and inverse FFT operationes are not lossless processes.
When you transform a signal you are dealing with floating
point numbers and you lose some information by rounding errors.
You could put some signal in the high freq portion of the
signal but it wont be as simple as XOR'ing values.

> 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.

This sounds interesting.  How about detection,  how will some
random phase relationships stand out against normal phase of
various frequencies?