The Vernam cipher is robust to small deviations from randomness

The Vernam cipher, or one-time pad, plays an important role in cryptography because it is perfectly secure. In this cipher a key is a sequence of equiprobable independently generated symbols. We show that under small disturbance of these properties the obtained cipher is close to the Vernam cipher in the case where the enciphered plaintext and the key are generated by stationary ergodic sources.