The Unicity Distance: An Upper Bound on the Probability of an Eavesdropper Successfully Estimating the Secret Key

The unicity distance, U, of a secret-key cipher is defined by Shannon as the minimum amount of intercepted ciphertext symbols needed, in principle, to uniquely determine the secret key and, therefore, break the cipher. Accordingly, for a ciphertext of size N symbols less than U, the estimated key will have a nonzero probability of error. Of interest is knowing the chance or probability that an eavesdropper, using the besf estimation rule, successfully estimates the secret key from N ciphertext symbols less than V. An upper bound on this probability is derived in this paper.