- Trifid cipher
In classical

cryptography , the**trifid cipher**is a cipher invented around 1901 byFelix Delastelle , which extends the concept of thebifid cipher to a third dimension, allowing each symbol to be fractionated into 3 elements instead of two. That is, while the bifid uses thePolybius square to turn each symbol into coordinates on a 5 × 5 (or 6 × 6) square, the trifid turns them into coordinates on a 3 × 3 × 3 cube. As with the bifid, this is then combined with transposition to achieve diffusion. However a higher degree of diffusion is achieved because each output symbol depends on 3 input symbols instead of two. Thus the trifid was the first practical trigraphic substitution.**Operation**First, a mixed alphabet cubic analogue of the Polybius square is drawn up:

In theory, the message is then converted to its coordinates in this grid; in practice, it is more convenient to write the triplets of trits out in a table, like so:Then the coordinates are written out vertically beneath the message:

**T R E A T Y E N D S B O E R W A R .**2 1 3 3 2 1 3 3 2 1 1 1 3 1 2 3 1 3 3 1 1 3 3 1 1 1 2 3 2 3 1 1 2 3 1 1 3 2 1 2 3 3 1 2 2 3 3 1 1 2 3 2 2 3They are then read out in rows:2 1 3 3 2 1 3 3 2 1 1 1 3 1 2 3 1 3 3 1 1 3 3 1 1 1 2 3 2 3 1 1 2 3 1 1 3 2 1 2 3 3 1 2 2 3 3 1 1 2 3 2 2 3

Then divided up into triplets again, and the triplets turned back into letters using the table: 213 321 332 111 312 313 311 331 112 323 112 311 321 233 122 331 123 223

**M U A F N . E Q R K R E U T X Q B W**In this way, eachciphertext character depends on threeplaintext characters, so the trifid is a trigraphic cipher. To decrypt, the procedure is simply reversed.**Dimensions**As the bifid concept is extended to higher dimensions, we are much less free in our choice of parameters.

Since $2^3\; =\; 8\; <\; 26\; <\; 27\; =\; 3^3$, our cube needs to have a side length of at least three in order to fit in the 26 letters of the alphabet. But if we go even to 4, then our symbol set would have $4^3\; =\; 64$ symbols, which is probably too much for classical cryptography. Thus, the trifid is only ever implemented with a 3 × 3 × 3 cube, and each coordinate is indicated by a trinary digit, or trit. Incidentally, note that since this gives us 27 symbols, we will have one extra. In the example above, the period or full-stop was used.

If we increase the dimensions further to four, noting that $2^4\; =\; 16\; <\; 26$, we still need a side length of 3 - giving a symbol set of size $3^4\; =\; 81$, far more than we need. If we go one step further, to five dimensions, then we only need a side length of 2, since $2^5\; =\; 32\; >\; 26$. But such a binary encoding - 5

bit s - is what occurs inBaudot code for telegraphic purposes. Breaking letters into bits and manipulating the bits individually is the hallmark of modern cryptography. Thus, in a sense, the trifid cipher can be thought to stand on the border between classical cryptography's ancientPolybius square , and the binary manipulations of the modern world.**See also*** Other ciphers by Delastelle:

**four-square cipher (related to Playfair)

**bifid cipher (similar to trifid)

*Wikimedia Foundation.
2010.*