Analogue Encryption, without converting to digital
Hello! I am thinking about analogue mobile telephones, but they have some severe flaws- the most significant being privacy.
How could an analogue system be encrypted? It doesn't need to be completely secure, but something that would make eavesdropping nearly impossible except with very complicated technology.
I don't want it to convert to digital for a short period (such as what the Cryptophon system, used by West Germany in the 1980s, did), but I am fine with a key being stored in digital form. Why do I not want it converted to digital at any point? I guess it just goes against "the vibes" of the setting, but also I'm sure I could make an excuse about cost measures due to low microchip production. This system is for civilian usage only, anyhow.
My current idea is that a digital key would be used to add noise to the signal, and the public key would be shared to the receiving phone when the answerer accepts the call- a short period of half a second before you can talk is acceptable to my mind. The phone at the other end would remove the noise using the public key. The signal in the other direction would be sent in the same way, with the key once again sent when the phone was answered.
So, to reword that: phone rings the other phone, when the other phone answers both phones quickly send the public keys out. Then, the phones might acknowledge the receiving of codes by repeating them back to check they got it right. Then, a small beep might sound to tell the user the call has started.
Is this idea solid? I don't know if it is, because I don't know too much about mathematics. I know early WWII systems using matching phonograph records could be cracked, but I think digital noise generators could be safer due to more complicated noise generation, as well as being much more versatile thanks to the digital key.
2 answers
It doesn't make much sense to talk about transmitting "keys" when the encryption is analog. Since you want to stay away from digital, the encryption and decryption will need to be done in analog hardware. That has a lot less flexibility than a digital algorithm, so the encryption needs to be more simplistic.
Look at how early "voice scramblers" were done. That seems to be exactly what you want.
Something analog circuitry can reasonably accomplish is messing with the signal in frequency space. This is basically what radio transmitters and receivers do. Your frequency space mangling needs to be a little more complicated than what common radio transmitters do, but not overly so in a world where such things are not widely understood, and there isn't something like today's internet where people who build decryptors can easily have access to others that want to use them.
Maybe the encryption uses three very specific frequencies to transform the voice frequencies with. Without the specific three frequencies in the receiver, the signal just sounds like gibberish to a human.
Consider how single sideband ham radio transmissions sound unless the receiver is closely tuned to the correct frequency. Now imagine you have to get three frequencies just right instead of one. That means you can't simply scan the band until it sounds right. With three frequencies, two of them would have to be close before scanning the third would yield anything useful. You'd be searching for a dot in 3-dimensional space, instead of 1-dimensional space like an ordinary radio.
Another technique is synchronous commutation. You flip polarity, or hetrodyne phase or something at intervals. The trick is to keep the receiver in sync so that it can do the unflipping at the right times.
Again, lots of stuff like this was done before it was feasible to transmit signals digitally.
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No, the scheme described doesn't make sense, regardless if it is digital or analog.
Anybody can intercept the public key and decrypt so the scheme doesn't protect against eavesdroppers. The entities are not authenticated either, so active attacks are also possible. To get a two side authenticated connection the system needs a key pair for which the public key is trusted by the other party.
That way an entity can authenticate itself. As long as that's possible then there are multiple ways of establishing a shared secret.
If you're looking for generic ways of applying analogue encryption you can have a look at this Q/A on Cryptography.SE.
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