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It seemed to have been tacitly assumed that this was an unavoidable principle of secret codes–for a cipher to be used the partners needed, somehow or other, to exchange the key to the cipher and to keep it secret from the enemy. Indeed, this might be regarded as mathematical common sense.
This is the kind of assumption that makes a mathematician suspicious. We are dealing with what is essentially a mathematical situation, so one would expect such a‘principle’to be well founded and represented by some form of mathematical theorem. Yet there was no such theorem, and the reason that there was no such theorem was that the principle simply is not valid, as the following thought experiment reveals.Transmission of a secure message from Alice to Bob does not in itself necessitate the exchange of the key to a cipher, for they can proceed as follows. Alice writes her plaintext message for Bob, and places it in a box that she secures with her own padlock. Only Alice has the key to this lock. She then posts the box to Bob, who of course cannot open it. Bob, however, then adds a second padlock to the box, for which he alone possesses the key. The box is then returned to Alice, who then removes her own lock, and sends the box for a second time to Bob. This time, Bob may unlock the box and read Alice’s message, secure in the knowledge that the meddling Eve could not have peeked at the contents during the delivery process. In this way, a secret message may be securely sent on an insecure channel without Alice and Bob ever exchanging keys. This imaginary scenario shows that there is no law that says that a key must change hands in the exchange of secure messages.In a real system, Alice and Bob’s‘locks’might be their own coding of the message rather than a physical device separating the would-be eavesdropper from the plaintext. Alice and Bob may then use this initial exchange to set up an ordinary symmetric cipher that would be used to mask all their future communication.