Re: Real-time sound cyphering algorithm

David Eather wrote:
> We are talking about recording a sound with a microphone.
> The microphone is like out ear only sensitive to pressure variations.
>
> Talking about power when the subject is volume is irrelevant.

I was talking about the transmitted carrier's signal-to-noise
ratio:

     So, correct me if I'm wrong: your solution is to transmit
     the sum of payload-sound plus a 20dB larger crypto-pseudo-
     random noise signal. Then the receiver subtracts off the
     crypto signal, to get the plaintext plus any noise on the
     transmission. For the sound to "be easily distinguished", we
     want the plaintext sound to be 20dB above the noise on the
     transmission channel. To get the payload 20dB above the
     noise, and the crypto-stream 20dB above the payload, we need
     an audio carrier with a signal-to-noise of 40dB, which is
     10,000-to-1 in sound power.

Transmission strength is universally expressed as power, not
pressure or voltage. More fundamentally, the carrier's
theoretical capacity in digits base d is:

     bandwidth * log_d(1 + S/N)

where S/N is signal power over the (Gaussian) noise power. The
10,000-to-1 signal-to-noise power ratio is vastly more important
than the 100-to-1 audio volume ratio.

[...]
> A conversation with the same error as BO's could go like this (sorry
> I can't think of the crypto equivalent)
>
> B1 "Power equals volts multiplied by current"
>
> B2 "Yeah great. What's the car battery voltage?"
>
> B1 "Five thousand watts"

Except that's the wrong subject. A talk with DE (who probably
likes his initials better than I like mine) might go:

E1: "How powerful is that radio station?"

E2: "5000 volts"

>>>OP wrote>
>>>I need the cyphered sound to be audible, but not understandable
>>
>>I think this can also be done by using a say 5kHz audio bandwidth
>>(more then enough for speech), and AM modulating a carrier at
>>20kHz. The lower sideband will go to 20 - 5 = 15 kHz.
>>You will hear some high peaked noises.
>>An other alternative is to use a FM carrier, and narrow band FM (so
>>use only one sideband), and use 10 kHz carrier :-)
>>This requires some filtering at the rx side, but any dsp board
>>should
>
> I like that idea. I would just suggest that it will not suit the OP
> in terms of resources and ease of implementation

In WWII, the U.S. and Briton used a slightly more sophisticated
idea along the same lines. Not only was it broken, with
training, operators could understand the signals directly. See:

     http://en.wikipedia.org/wiki/Single-sideband_modulation

-- 
--Bryan