On 2006-04-22, Udhay Shankar N wrote:
I found this off a link from Schneier's newsletter. Can anybody
comment on this?
Passive, linear, time-invariant, nondissipative systems are essentially
allpass networks which simply redistribute energy in time and outputs.
Like all LTI systems they can be completely specified in terms of their
response to impulses but in this particular case the system is also
extremely easy to invert: you just reverse both the system (outputs
become inputs) and its impulse response (first sample becomes the last).
Systems which respond approximately this way abound in acoustics,
optics, circuit design, digital signal processing and who knows where.
In time reversal acoustics the input is typically some pointlike
acoustic phenomenon like a spark, the output is a set of microphone
signals and the system is some propagation medium with little absorption
but an unlimited amount and complexity of internal reflections. The
response of such a system in time and space can be accurately compared
to what spread spectrum modulation does to a signal in the frequency
domain: energy is spread in a complex but essentially linear fashion.
Inverting the system by time reversion recompacts the energy at the
original source so that the reverse system can be used as a spatially
and temporally randomized focusing device/lens despite its complexity.
And since there is no essential limit to the complexity, area or (to a
lesser amount) temporal extent of the system response, the achievable
spreading can be large enough to hide the decompacted signal under the
local noise floor of the surrounding acoustic environment while still
allowing recompaction at the focal point. Such spatial-temporal
de/spreading is probably the cryptographic application that was
imagined; its prime weakness is probably in the linearity of the
primitive.
So in a sense this is nothing new. Direct sequence spread spectrum has
been used for decades now, systems as different as synthetic aperture
radars, beamforming sonars and laser pulse compressor gratings do energy
compaction all the time, and holographic crypto -- another highly
dispersive physical system with a unitary response -- exists as a
concept in literature. At least to me it seems that the most interesting
parts of this are the realizations that a) highly dispersive media can
be used as somewhat lossy collectors/focusing lenses with any point as
the focal point provided their response can be inverted, b) such
physical operations are available in the acoustic domain too and c) it
might be possible to construct such media in a difficult to duplicate,
one-shot fashion and then use them as computationally heavy black boxes
in algorithms. (The latter part is analogous to efforts at creating
physical one-time tokens for watermarking purposes.)
--
Sampo Syreeni, aka decoy - mailto:[EMAIL PROTECTED], tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2
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