Can you explain to me how Vigenère cyphers are supposed to work

Factual Questions
1

Wikipedia page here Vigenère cipher - Wikipedia
show this example
Plaintext: ATTACKATDAWN
Key: LEMONLEMONLE
Ciphertext: LXFOPVEFRNHR
I won’t reproduced the tabula recta here but it has the normal (un-keyed) alphabet running horizontally along the top from left to right and another one running vertically down the left hand side. Lets call them the “heading” alphabets. The displaced alphabets fill the square of text that is in between.

OK, in the example shown on wiki in order to decrypt a message you use the first letter of the keyword (“L)” to find the alphabet at position “L”, then find within that alphabet the first word of the cipher (in this case also “L”) then look up to the top heading alphabet to find the plaintext letter (“A”).

Fine.

But the Vigenère cypher Kryptos at the CIA doesn’t work like that, and if you try that way on it it fails to decrypt. The keyword is PALIMPSEST. It seems the CIA cypher one doesn’t use the heading alphabets (even though it has them) instead it uses the displaced alphabets directly.

So if I were to make my own Vigenère cypher, and for it to be solvable, how would anyone know which method to use?

2

Here is the CIA’s variant illustrated. You will remark that there are two keywords used: KRYPTOS and PALIMPSEST, and that the tabula recta is modified accordingly.

If you create your own cyphertext as a puzzle, obviously it will be easier to decrypt if you use a single keyword and the vanilla method described in the Wikipedia article. Both will be “solvable” though, especially using a computer.

3

So the wikipedia way is the standard way then?

And the CIA one was just some weird variant that people had to guess at?

4

Historically there have been lots of variants in Vigenère ciphers. The Wikipedia example is the most basic kind, but people have come up with all sorts of modifications. (Most of them are not very strong, but this was before modern cryptanalysis and computers.)

The CIA sculpture isn’t the first to use multiple keywords, so cryptography enthusiasts were well acquainted with that technique and able to solve the first two passages fairly quickly.

5

I actually did see that but it wasn’t very helpful to me. It doesn’t show how the letters PALIMPSEST are inserted into the tabula recta. Can you explain it to me please? Do they displace letters (by transposition) that were already there or replace them? In a vertical or a horizontal direction?

What I’m basically saying is that the tabula in that link you sent is not the same tabula that is at the CIA. What changes have been made? Thanks.

6

Oh I see it now. They didn’t insert PALIMPSEST like they did KRYPTOS.