# Trifid cipher

Trifid cipher

In classical cryptography, the trifid cipher is a cipher invented around 1901 by Felix Delastelle, which extends the concept of the bifid cipher to a third dimension, allowing each symbol to be fractionated into 3 elements instead of two. That is, while the bifid uses the Polybius square to turn each symbol into coordinates on a 5 &times; 5 (or 6 &times; 6) square, the trifid turns them into coordinates on a 3 &times; 3 &times; 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 WIn this way, each ciphertext character depends on three plaintext 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 &times; 3 &times; 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 bits - is what occurs in Baudot 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 ancient Polybius square, and the binary manipulations of the modern world.

* Other ciphers by Delastelle:
** four-square cipher (related to Playfair)
** bifid cipher (similar to trifid)

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