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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](http://www.cryptomuseum.com/crypto/bbc/cryptophon/index.htm) 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.