Editing Vigenère cipher (section)

===Running key===
The [[running key cipher|running key]] variant of the Vigenère cipher was also considered unbreakable at one time. For the key, this version uses a block of text as long as the plaintext. Since the key is as long as the message, the Friedman and Kasiski tests no longer work, as the key is not repeated.

If multiple keys are used, the effective key length is the [[least common multiple]] of the lengths of the individual keys.  For example, using the two keys <code>GO</code> and <code>CAT</code>, whose lengths are 2 and 3, one obtains an effective key length of 6 (the least common multiple of 2 and 3).  This can be understood as the point where both keys line up.

{|
| Plaintext: || <code>attackatdawn</code>
|-
| Key 1: || <code>GOGOGO'''GOGOGO'''</code>
|-
| Key 2: || <code>CATCAT'''CATCAT'''</code>
|-
| Ciphertext: || <code>IHSQIRIHCQCU</code>
|}

Encrypting twice, first with the key <code>GO</code> and then with the key <code>CAT</code> is the same as encrypting once with a key produced by encrypting one key with the other.

{|
| Plaintext: || <code>gogogo</code>
|-
| Key: || <code>CATCAT</code>
|-
| Ciphertext: || <code>IOZQGH</code>
|}

This is demonstrated by encrypting <code>attackatdawn</code> with <code>IOZQGH</code>, to produce the same ciphertext as in the original example.

{|
| Plaintext: || <code>attackatdawn</code>
|-
| Key: || <code>IOZQGHIOZQGH</code>
|-
| Ciphertext: || <code>IHSQIRIHCQCU</code>
|}

If key lengths are relatively prime, the effective key length is the product of the key lengths, and hence grows quickly as the individual key lengths are increased. For example, while the effective length of combined key lengths of 10, 12, and 15 characters is only 60 (2x2x3x5), that of key lengths of 8, 11, and 15 characters is 1320 (8x11x15).  If this effective key length is longer than the ciphertext, it achieves the same immunity to the Friedman and Kasiski tests as the running key variant.

If one uses a key that is truly random, is at least as long as the encrypted message, and is used only once, the Vigenère cipher is theoretically unbreakable.  However, in that case, the key, not the cipher, provides cryptographic strength, and such systems are properly referred to collectively as [[one-time pad]] systems, irrespective of the ciphers employed.

[[File:Confederate cipher wheel (Vigenere), captured at the surrender of Mobile, Alabama, in May 1865 - National Cryptologic Museum - DSC07710.JPG|thumb|left|Confederate cipher wheel, captured at the surrender of [[Mobile, Alabama]], in May 1865 – [[National Cryptologic Museum]]]]