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 co-ordinates on a 5 × 5 (or 6 × 6) square, the trifid turns them into co-ordinates 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.

Dimensions

As the bifid concept is extended to higher dimensions, we are much less free in our choice of parameters.

Since 2³ = 8 < 26 < 27 = 3³, 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 4³ = 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 co-ordinate is indicated by a trinary digit, or trit. Incidentally, note that since this gives us 27 symbols, we will have one spare. In this example, we will use the period, or full-stop.

If we increase the dimensions further to four, noting that 2⁴ = 16 < 26, we still need a side length of 3 - giving a symbol set of size 3⁴ = 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 2⁵ = 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.

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 co-ordinates 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 3

They 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, each ciphertext character depends on three plaintext characters, so the trifid is a trigraphic cipher. To decrypt, the procedure is simply reversed.

See also

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