Even in the 1960's most Soviet radio traffic would have been encrypted. That was why the US did things like Ivy Bells (1), because they wouldn't be encrypting domestic phone traffic. (They were able to get information on Soviet missile tests, after the fact, from that source.)
And of course, as always, the easiest way to break a code is always the 5 dollar wrench attack (something like the way the Soviets paid the Walker spy ring a few thousand dollars a month to just give them the decryption keys (2)).
Finally, there is Radio MASINT that also gathers information from radio receivers, even if they are encrypted (3).