Editing Information theory (section)

===Intelligence uses and secrecy applications===
{{Unreferenced section|date=April 2024}}
Information theoretic concepts apply to cryptography and cryptanalysis. Turing's information unit, the [[Ban (unit)|ban]], was used in the [[Ultra (cryptography)|Ultra]] project, breaking the German [[Enigma machine]] code and hastening the [[Victory in Europe Day|end of World War II in Europe]]. Shannon himself defined an important concept now called the [[unicity distance]]. Based on the redundancy of the [[plaintext]], it attempts to give a minimum amount of [[ciphertext]] necessary to ensure unique decipherability.

Information theory leads us to believe it is much more difficult to keep secrets than it might first appear. A [[brute force attack]] can break systems based on [[public-key cryptography|asymmetric key algorithms]] or on most commonly used methods of [[symmetric-key algorithm|symmetric key algorithms]] (sometimes called secret key algorithms), such as [[block cipher]]s. The security of all such methods comes from the assumption that no known attack can break them in a practical amount of time.

[[Information theoretic security]] refers to methods such as the [[one-time pad]] that are not vulnerable to such brute force attacks. In such cases, the positive conditional mutual information between the plaintext and ciphertext (conditioned on the [[key (cryptography)|key]]) can ensure proper transmission, while the unconditional mutual information between the plaintext and ciphertext remains zero, resulting in absolutely secure communications. In other words, an eavesdropper would not be able to improve his or her guess of the plaintext by gaining knowledge of the ciphertext but not of the key. However, as in any other cryptographic system, care must be used to correctly apply even information-theoretically secure methods; the [[Venona project]] was able to crack the one-time pads of the Soviet Union due to their improper reuse of key material.