The unicity distance: An upper bound on the probability of an eavesdropper successfully estimating the secret key

Abstract

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 best estimation rule , successfully estimates the secret key from N ciphertext symbols less than U . An upper bound on this probability is derived in this paper.