Cryptology Running-Text Ciphers with Random Keys

a7Hzq .#5r< kÜ\as TâÆK$ ûj(Ö2 ñw%h: Úk{4R f~`z8 ¤˜Æ+Ô „&¢Dø

All cryptanalytic methods collapse when the key is a random letter sequence, chosen in an independent way for each plaintext, and never repeated.

In particular all the letters in the ciphertexts occur with the same probability. Or in other words, the distribution of the ciphertext letters is completely flat.

This encryption method is called One-Time Pad (OTP). Usually Gilbert VERNAM (1890-1960) is considered as the inventor in the World War I year 1917. But the idea of a random key is due to MAUBORGNE who improved VERNAM's periodic XOR cipher in this way. The German cryptologists KUNZE, SCHAUFFLER, and LANGLOTZ in 1921—presumably independently—proposed the »individuellen Schlüssel« (»individual key«) for running-text encryption of texts over the alphabet {A, ..., Z}.

In other words: The idea »was in the air«. In 2011 Steve Bellovin discovered a much earlier proposal of the method by one Frank MILLER in 1882 who however was completely unknown as a crypologist and didn't have any influence on the history of cryptography.

Steven M. Bellovin. Frank Miller: Inventor of the One-Time Pad. Cryptologia 35 (2011), 203–222.

The mathematical version of this section contains evidence for the security of using random keys. The general idea is:

»Something + Random = Random« or »Chaos Beats Order« (Children's Room Theorem)

Discussion

The theorem says that a One-Time Pad encryption results in a ciphertext that »has nothing to do« with the plaintext, in particular doesn't offer any lever for the cryptanalyst.

Why then isn't the One-Time Pad the universally accepted standard method of encryption?

• Agreeing upon a key is a major problem—if we can securely transmit a key of this length, why not immediately transmit the message over the same secure message channel? Or if the key is agreed upon some time in advance—how to remember it?
• The method is suited at best for a two-party communication. For a multiparty communication the complexity of key distribution becomes prohibitive.
• When the attacker has known plaintext she is not able to draw any conclusions about other parts of the text. But she can exchange the known plaintext with another text she likes more: The integrity of the message is at risk.