Computer Security and Cryptography

4.4 THE ONE-TIME PAD

Major Joseph O. Mauborgne began his study of cryptanalysis at the U.S. Army's Signal School, located at Fort Leavenworth (Kansas), later becaming Chief Signal Officer and the director of the Signal Corp's Engineering and Research Division.

When Vernam's cryptographic invention was reported by AT&T to the U.S. Army, Major Mauborgne recognized its importance. He also understood that the reuse of a long tape might make Vernam-ciphertext vulnerable to cryptanalysis. U.S. Patent 1,310,719, filed by Vernam and Mauborgne, described their one-time tape generalization of the AT&T additive polyalphabetic encipherment system.

A one-time tape system uses the key additively as Vernam proposed, but each key value enters in the encipherment of only one plaintext character. A one-time system can be defined for plaintext written in any alphabet, but as alphanumeric ASCII text is always coded into sequences of 0's and 1's prior to transmission or storage, we may assume the plaintext and ciphertext alphabet letters are 0's and 1's.

Let (x₀, x₁, x₂, …, x_n−1) be any sequence of 0's and 1's with no assumption of any kind made about the statistical distribution of value of the sequence. A Bernoulli process³ is a random process consisting of a sequence of independent and identically distributed (0,1)-valued random variables, which may be imagined to arise from repeatedly and independently tossing a fair-coin:

The one-time encipherment of plaintext x₀, x₁, x₂, …, x_n−1 by a Bernoulli ...