As I understand the Rabin proposal, it addresses Shannon. The biggest
impracticality with Shannon is the problem of key material. As the
amount of traffic goes up, the requirement for key material goes up
proportionally, i.e., one for one. As that happens, the necessary
conditions for proof beome increasingly difficult to meet, the cost of
encryption increases, and the value decreases. It becomes increasingly
difficult to generate the keying material, to ensure that it is random,
and to know that it is used only once. As the amount of key material
goes up, storing and managing it becomes more difficult. As the amount
of material increases, so do the cost and difficulty of exchanging it
securely. As you suggest, the problem begins to approximate that of
exchanging the messages securely. Said another way, the solution
becomes the problem.

Rabin attributes this to the fact that the quantity of keying material
is equal to the quantitiy of the traffic, a problem which conventional
cryptography does not have. Rabin asks, "How might we have the
provability of Shannon with the limited amount of pre-arrangement of
conventional cryptography?" The intent of his proposal seems to be to
answer that question. As you note, it introduces problems of its own.

"There is no such thing as a free lunch."

-Asbestos

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