Actually, why not just broadcast, in clear, "The codes have been compromised and all transmissions this morning are false"?? Might at the very least cause the operatives in the field to pause and try to confirm their orders.
And actually, I think that the whole premise of the film is faulty. One-time-pad cyphers really are unbreakable, and I don't see any need for any sort of analyst or broadcaster at a facility like this. One copy of the pad of course belongs to the agents in the field, and the other copy is in the hands of their masters in Washington, Langley, Ft. Meade, or wherever. Having another copy at the transmitting station, or any sort of enciphering/deciphering capability, or any sort of cryptorapher/analyst, would definitely compromise security. So all that hand-waving about hidden codes from Meredith to unlock programs that encipher the messages (or whatever seemed to be going on) would be total nonsense.
The spy bosses use their copies of the pads to encipher their orders, and send the numbers to the various stations, where a synthesized voice reads them out. Certainly there would be a need for minders to keep the transmitters safe and the transmitter tubes warm (so to speak), but not much use for any computer stuff outside of a speech synthesizer. (In addition, any sensible outfit running such an operation would try to pad the transmissions with null messages around the clock, so any listeners would be unable to detect whether the traffic is increasing; this might be a little hard on human broadcasters.)
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