NSA Technical Journal published "The Unbreakable Cipher" in Spring
   1961.
   [1]http://www.nsa.gov/public_info/_files/tech_journals/The_Unbreakable_
   Cipher.pdf
   Excerpts:
   [Quote]
   David Kahn, "Lyen Otuu Wllwgh WI Etjown" pp. 71, 83, 84, 86,
   88 and 90 of the New York Times Magazine November 13, 1960
   says that an unbreakable cipher system can be made from one
   time key "that is absolutely random and never repeats."  ...
   For each cipher system there is an upper bound to the amount of
   traffic it can protect against cryptanalytic attack. What is
   "cryptanalytic attack"? It is a process applied to cipher text
   in order to extract information, especially information
   contained in the messages and intended to be kept secret.
   If some of the information is gotten by other means and this
   results in more being extracted from the cipher, this is (at
   least partially) a successful attack. If certain phrases can be
   recognized when they are present, this is successful cryptanalysis.
   If a priori probabilities on possible contents are altered by
   examination of the cipher, this is cryptanalytic progress.
   If in making trial decipherments it is possible to pick out
   the correct one then cryptanalysis is successful. ...
   Another example is that of Mr. Kahn, one-time key. Here the
   limit is quite clear; it is the amount of key on hand. The key arrives
   in finite "messages," so there is only a finite amount on hand at
   anyone time, and this limits the amount of traffic which can be sent
   securely. Of course another shipment of key raises this bound, but
   technically another cipher system is now in effect, for by my
   definition a cipher system is a message. A sequence of messages
   is a sequence of cipher systems, related perhaps, but not the same. ...
   [Answer to the question:] "Does there exist an unbreakable cipher"
   would be this, "Every cipher is breakable, given enough traffic, and
   every cipher is unbreakable, if the traffic volume is restricted
   enough."
   [End quote]
   Is this conclusion still valid? If so, what could be done to restrict
   traffic
   volume to assure unbreakablility? And how to sufficiently test that.
   Presuming that NSA and cohorts have investigated this effect.

References

   1. http://www.nsa.gov/public_info/_files/tech_journals/The_Unbreakable_Cipher.pdf