They could just create an in-house LAN [Local Area Network] and make sure it is NOT tied into the Internet.
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With typewriters, NSA could reposition a high-tech satellite to ‘listen’ in on the typing. Each key does have a distinctive different sound. With modern software, NSA could decode the keystrokes and reveal what was typed.
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The best alternative would be: smoke signals.
They could use smoke signals and have a high-speed fan to dissipate the smoke before the NSA satellite could decipher it.
Cones of silence for each station. Seal in the operator and typewriter.