Editing Cryptanalysis (section)

====Depth====
Sending two or more messages with the same key is an insecure process. To a cryptanalyst the messages are then said to be ''"in depth."''<ref>{{Harvnb|Churchhouse|2002|p=34}}</ref><ref>The [[Bletchley Park]] 1944 Cryptographic Dictionary defined a depth as <br /> 1. A series of code messages reciphered with the same, or the same part of a, reciphering key especially when written under one another so that all the groups (usually one in each message) that are reciphered with the same group of the subtractor lie under each other and form a 'column'.<br /> (b) two or more messages in a transposition cipher that are of the same length and have been enciphered on the same key;<br /> (c) two or more messages in a machine or similar cipher that have been enciphered on the same machine-setting or on the same key.<br /> 2. be in depth: (of messages). Stand to each other in any of the relationships described above.<br />{{Citation |title=The Bletchley Park 1944 Cryptographic Dictionary formatted by Tony Sale (c) 2001 |page=27 |url=https://www.codesandciphers.org.uk/documents/cryptdict/cryptxtt.pdf}}</ref> This may be detected by the messages having the same ''[[Enigma machine#Indicator|indicator]]'' by which the sending operator informs the receiving operator about the [[Key (cryptography)|key generator initial settings]] for the message.<ref>{{Harvnb|Churchhouse|2002|pp= 33, 86}}</ref>

Generally, the cryptanalyst may benefit from lining up identical enciphering operations among a set of messages. For example, the [[Gilbert Vernam|Vernam cipher]] enciphers by bit-for-bit combining plaintext with a long key using the "[[exclusive or]]" operator, which is also known as "[[Modular arithmetic|modulo-2 addition]]" (symbolized by ⊕ ):
::::Plaintext ⊕ Key = Ciphertext
Deciphering combines the same key bits with the ciphertext to reconstruct the plaintext:
::::Ciphertext ⊕ Key = Plaintext
(In modulo-2 arithmetic, addition is the same as subtraction.) When two such ciphertexts are aligned in depth, combining them eliminates the common key, leaving just a combination of the two plaintexts:
::::Ciphertext1 ⊕ Ciphertext2 = Plaintext1 ⊕ Plaintext2
The individual plaintexts can then be worked out linguistically by trying ''probable words'' (or phrases), also known as ''"cribs,"'' at various locations; a correct guess, when combined with the merged plaintext stream, produces intelligible text from the other plaintext component:
::::Cyphertext1 ⊕ Cyphertext2 ⊕ Plaintext1 = Plaintext2
The recovered fragment of the second plaintext can often be extended in one or both directions, and the extra characters can be combined with the merged plaintext stream to extend the first plaintext. Working back and forth between the two plaintexts, using the intelligibility criterion to check guesses, the analyst may recover much or all of the original plaintexts. (With only two plaintexts in depth, the analyst may not know which one corresponds to which ciphertext, but in practice this is not a large problem.) When a recovered plaintext is then combined with its ciphertext, the key is revealed:
::::Plaintext1 ⊕ Ciphertext1 = Key
Knowledge of a key then allows the analyst to read other messages encrypted with the same key, and knowledge of a set of related keys may allow cryptanalysts to diagnose the system used for constructing them.<ref name="Tutte 1998"/>