Conditionally-perfect secrecy and a provably-secure randomized cipher

Shannon's pessimistic theorem, which states that a cipher can be perfect only when the entropy of the secret key is at least as great as that of the plaintext, is relativized by the demonstration of a randomized cipher in which the secret key is short but the plaintext can be very long. Two modifications of this cipher are discussed that may lead to practical provably-secure ciphers based on either of two assumptions that appear to be novel in cryptography, viz., the (sole) assumption that the enemy's memory capacity (but not his computing power) is restricted and the assumption that an explicit function is, in a specified sense, controllably-difficult to compute, but not necessarily one-way.