From: Eli Brandt <ebrandt@jarthur.Claremont.EDU>
Date: Sun, 19 Sep 93 23:19:51 PDT
To: cypherpunks@toad.com
Subject: Re: Stegno and DAT and digital music...
In-Reply-To: <199309131414.AA07464@access.digex.net>
Message-ID: <9309200619.AA25512@toad.com>
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> improved the sound. He says that the original CD format was
> limited to 16 bits of sound because of costs. But many audiophiles
> reacted very negatively to the tinny, metalic quality to the music.

Heh.  Lack of sufficient bits for digital sound results in a floor of
uniformly-distributed white noise for complex signals such as music.
If audiophiles really hear "tinny" or "metallic" sound in double-blind
tests, it would more likely be due to the sampling rate.  The 44kHz
rate means that skimping on the lowpass filter will push the cutoff
into the audible range, which means you lose some upper harmonics and
get to hear any phase nonlinearity in the filter.

> For this reason, the companies have developed 20 bit DAT recording
> tape and then come up with ways to "dither" this into 16 bits. 
> 
> I am curious if anyone knows the details of these algorithms. 

Round to 16 bits.  The higher-precision recording format is good
because it lets noise (e.g. from mixing up a quiet signal) chew off
four bits before it gets on the CD.  You can do a little better than
rounding, but not much.

> Also, his point suggests that flipping the least significant 
> bit of 16 bit music may not be imperceptable to some ears.

It may well not be, particularly if you do it without regard to the
piece's amplitude.  That 6dB of hiss may be perceptible during
pauses.

A more subtle flaw is that the signal will have artificial statistical
characteristics.  Natural noise in recordings is typically Gaussian,
not uniform noise covering exactly one bit.  What this means is that
if the LSB is total uncorrelated hash, the bit above will have some
noise.  Look at a quiet passage.  If the LSB is noise city and the
14th is uniformly zero, somebody twiddled with the digital data.  This
is a more reasonable way of screening for this sort of steganography
than hiring a bunch of audiophiles.  

One fix is to cover your nefarious LSB activities by first adding
sufficient Gaussian noise.  My intuition, however, is that any amount
short of microwaving the CD will leave a little bit of correlation
between the original and the noised lower bits.  With sufficient data,
I think you can burn through the Gaussian noise and get enough
information to make a call on whether the LSB has been twiddled.  And
a CD is a lot of data.

> -Peter Wayner

   Eli   ebrandt@jarthur.claremont.edu