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"You need some technical sophistication to use these things successfully."

There is a very low-tech yet unbreakable method. You and someone agree on a book in both of your homes. You send a series of numbers that reference a page, paragraph, sentence, and letter or punctuation position. To break the code you must know the book title, which number is the page, which is the paragraph (if you use it), which number is the sentence, and which number is the actual character etc.. In using this method, repeating the same letter will generate a completely different sequence of numbers each time.

Unless you or the other person tells the government what book you are using they cannot break the code.

For example if I sent you 2,1,34,6,10,7,1,26,4,22,4,20,3,9,1,37,1,1 I doubt if any of our alphabet government agencies could tell you what I sent.

Sending a unique value say 78 would tell the person to change the order of page,paragraph,sentence,character. If you want to protect it further you could apply some encryption to it but that usually means you have to have a copy of the code somewhere and the whole purpose of this method is to prevent anyone from finding the encryption key.

The only caveat with this method is to choose a book or books that would be common to many homes not something unique like the collected wisdom of Hillary Clinton, which only has 1 blank page.

Someone has already suggested a similar approach, though a bit more high tech. What you're describing is a series of "one time pads"; keys that are used only once and then tossed. These are great unless someone compromises the book of code sheets. A researcher recently suggested using a continuous stream of data as the source for the one time pads. Users would simply pick a particular moment in time to start collecting data from the stream to generate the keys. When they're done, they discard the data. The next time the want to encrypt data, they go back to the stream and collect more data for a fresh set of keys. So long at the agreed upon time to start collecting data is kept secure, the given message is secure; even though the data stream is being broadcast to the general public. (Except, of course, from brute force attacks. But all codes are eventually suceptible to brute force attacks.)