Editing Trifid cipher (section)

== Description ==

As discussed above, the cipher requires a 27-letter mixed alphabet: we follow Delastelle by using a plus sign as the 27th letter.<ref>Delastelle, p. 102: "Mais l'alphabet français ne contenant que vingt-six lettres…"</ref> A traditional method for constructing a mixed alphabet from a key word or phrase is to write out the unique letters of the key in order, followed by the remaining letters of the alphabet in the usual order.<ref>See [[substitution cipher]].</ref> For example, the key FELIX MARIE DELASTELLE yields the mixed alphabet FELIXMARDSTBCGHJKNOPQUVWYZ+.

To each letter in the mixed alphabet we assign one of the 27 trigrams (111, 112, …, 333) by populating a 3 × 3 × 3 cube with the letters of the mixed alphabet, and using the [[Cartesian coordinates]] of each letter as the corresponding trigram.

{| class="wikitable"
! colspan="4" | Layer 1 
|
! colspan="4" | Layer 2 
|
! colspan="4" | Layer 3
|-
! || 1 || 2 || 3 
| 
! || 1 || 2 || 3 
| 
! || 1 || 2 || 3
|-
! 1 
| F || E || L || 
! 1 
| S || T || B || 
! 1 
| O || P || Q
|-
! 2 
| I || X || M || 
! 2 
| C || G || H || 
! 2 
| U || V || W
|-
! 3 
| A || R || D || 
! 3 
| J || K || N || 
! 3
| Y || Z || +
|}

From this cube we build tables for enciphering letters as trigrams and deciphering trigrams as letters:

{| class="wikitable"
! colspan="3" | Enciphering alphabet ||
! colspan="3" | Deciphering alphabet 
|-
| A = 131 || J = 231 || S = 211 ||
| 111 = F || 211 = S || 311 = O
|-
| B = 213 || K = 232 || T = 212 ||
| 112 = E || 212 = T || 312 = P
|-
| C = 221 || L = 113 || U = 321 ||
| 113 = L || 213 = B || 313 = Q
|-
| D = 133 || M = 123 || V = 322 ||
| 121 = I || 221 = C || 321 = U
|-
| E = 112 || N = 233 || W = 323 ||
| 122 = X || 222 = G || 322 = V
|-
| F = 111 || O = 311 || X = 122 ||
| 123 = M || 223 = H || 323 = W
|-
| G = 222 || P = 312 || Y = 331 ||
| 131 = A || 231 = J || 331 = Y
|-
| H = 223 || Q = 313 || Z = 332 ||
| 132 = R || 232 = K || 332 = Z
|-
| I = 121 || R = 132 || + = 333 ||
| 133 = D || 233 = N || 333 = +
|}

The encryption protocol divides the plaintext into groups of fixed size (plus possibly one short group at the end): this confines encoding errors to the group in which they occur,<ref>Gaines, p. 210.</ref> an important consideration for ciphers that must be implemented by hand. The group size should be [[Coprime integers|coprime]] to 3 to get the maximum amount of diffusion within each group: Delastelle gives examples with groups of 5 and 7 letters. He describes the encryption step as follows:<ref>Delastelle, p. 102: "Nous commençons par inscrire ''verticalement'' sous chaque lettre…"</ref><blockquote>We start by writing ''vertically'' under each letter, the numerical trigram that corresponds to it in the enciphering alphabet: then proceeding ''horizontally'' as if the numbers were written on a single line, we take groups of three numbers, look them up in the deciphering alphabet, and write the result under each column.</blockquote>

For example, if the message is ''[[aide-toi, le ciel t'aidera]]'', and the group size is 5, then encryption proceeds as follows:

 ''a i d e-t   o i l e c   i e l t'a   i d e r a''
 1 1 1.1 2   3 1 1.1 2   1 1 1.2 1   1 1 1.1 1
 3.2 3 1.1   1.2 1 1.2   2.1 1 1.3   2.3 1 3.3
 1 1.3 2 2   1 1.3 2 1   1 2.3 2 1   1 3.2 2 1
 '''F M J F V   O I S S U   F T F P U   F E Q Q C'''

In this table the periods delimit the trigrams as they are read horizontally in each group, thus in the first group we have 111 = F, 123 = M, 231 = J, and so on.