Continued...

The recipient has a copy of the same pad, and uses the same set of random numbers to decrypt the message (in this case subtracting the random number from the transmitted number to produce the plaintext.

As you can see, the secret is the use of a set of random numbers to encrypt the message. Other encryption schemes can be broken because if an algorithm is used to encrypt the message, it is possible to deduce that algorithm. With the one time pad, purely random numbers are used. There's no algorithm to generate them, so there's nothing to break. Of course, this assumes that truly random numbers are used. Sophisticated techniques
are available for producing random numbers, including the decay of radioisotopes. I also understand that CDROMS are available which contain nothing but random numbers. The random number generators in most personal computers do use rather poor algorithms which don't produce truly random numbers.

As the name implies, the secret is that the pad is only to be used once. This ensures that enough ciphertext is not available to make use of statistical code breaking methods. And, should that code become compromised, no other messages are subject to decryption.

And as it turns out, the pads are actually physically quite small. Russian pads by the 1960's were the size of postage stamps (read with a magnifying glass). Later they became microdots, requiring a microscope to read them. This made it possible to hide them quite easily. The pad could literally be the period at the end of a sentence in a letter! This allowed the pads to be easily conveyed to agents in the field.

As it turns out, one time pad systems have been broken. Perhaps the best publicized case is the decoding of Soviet KGB and GRU messages during World War II by American code breakers. Information about the VENONA project is available on the NSA web page. Supposedly, the Soviets broke the cardinal rule of one time pads, they used them more than once!

So, how do Spy Number Stations encode their messages. Due to the relatively short messages (sometimes 20 or so groups) often heard, it is unlikely that individual letters are encoded. It is possible that each group represents a word, or perhaps even some represent common phrases. Some groups could represent individual letters, for when it is necessary
to spell out a name or location. It is also possible that some common words or phrases can be represented by more than one group, this should make attacks on the code much less sucessful.

With a five digit code, 100,000 possible words or phrases could be encoded. A four digit code could encode 10,000 possible words or phrases. But that brings up an interesting point. Just because the message is sent as blocks of four or five digit numbers does not mean that is the actual entryption system used! It is quite possible that they are
transmitted that way to make it easier for the agent to copy the message. People deal with short numbers much better than long ones. The actual encryption system could make use of six digit numbers, with 1,000,000 possibities. This would allow practically every word in the English language to be encoded.

Many descriptions of cryptography that I've read often display ciphertext in five character/digit blocks, so this seems to be standard. That being the case, the fact that Spy Number Stations transmit messages in five (or sometimes four) digit blocks probably has nothing to do with the actual size of each unit of ciphertext.

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