Editing Lorenz cipher (section)

==Vernam cipher==
{{Main|Gilbert Vernam}}
[[Gilbert Vernam]] was an [[AT&T Corporation|AT&T]] [[Bell Labs]] research engineer who, in 1917, invented a cipher system in which the plaintext bitstream is enciphered by combining it with a random or pseudorandom bitstream (the "keystream") to generate the ciphertext. This combination is done using the [[Boolean algebra (logic)|Boolean]] [[Exclusive or|"exclusive or" (XOR)]] function, symbolised by ⊕.<ref>{{Harvnb|Klein|p=2}}</ref> This is represented by the following "[[truth table]]", where 1 represents "true" and 0 represents "false".

{| class="wikitable" style="text-align:center; margin: 0 auto"
|+ XOR truth table
|-
!colspan="2" | Input || rowspan="2" style="width: 70px;" | A ⊕ B
|-
!style="width: 45px;" | A || style="width: 45px;" | B
|-
| 0 || 0 || 0
|-
| 0 || 1 || 1
|-
| 1 || 0 || 1
|-
| 1 || 1 || 0
|}

Other names for this function are: Not equal (NEQ), [[Modular arithmetic|modulo]] 2 addition (without 'carry') and modulo 2 subtraction (without 'borrow').

Vernam's cipher is a [[symmetric-key algorithm]], i.e. the same [[Key (cryptography)|key]] is used both to encipher [[plaintext]] to produce the [[ciphertext]] and to decipher ciphertext to yield the original plaintext:

{{block indent|1=plaintext ⊕ key = ciphertext}}

and:

{{block indent|1=ciphertext ⊕ key = plaintext}}

This produces the essential reciprocity that allows the same machine with the same settings to be used for both encryption and decryption.

Vernam's idea was to use conventional telegraphy practice with a paper tape of the plaintext combined with a paper tape of the key. Each key tape would have been unique (a [[One-time pad|one-time tape]]), but generating and distributing such tapes presented considerable practical difficulties. In the 1920s four men in different countries invented rotor cipher machines to produce a key stream to act instead of a tape.<ref>{{Harvnb|Klein|p=3}}</ref> The 1940 Lorenz SZ40/42 was one of these.<ref name = "GRoT11B10">{{Harvnb|Good|Michie|Timms|1945|p=10}} of ''German Tunny''</ref>