Trifid cipher

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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.

Contents 1 Operation 2 Dimensions 3 See also 4 External Links

[edit] Operation

First, a mixed alphabet cubic analogue of the Polybius square is drawn up:

Layer 1					Layer 2					Layer 3
	1	2	3			1	2	3			1	2	3
1	F	J	O		1	V	Z	L		1	E	U	Q
2	R	X	C		2	G	D	P		2	N	H	A
3	Y	B	S		3	M	W	T		3	.	K	I

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:

F 111	C 132	W 223	U 321
R 112	S 133	L 231	H 322
Y 113	V 211	P 232	K 323
J 121	G 212	T 233	Q 331
X 122	M 213	E 311	A 332
B 123	Z 221	N 312	I 333
O 131	D 222	. 313

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.

[edit] 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 extra. In the example above, the period or full-stop was used.

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.

[edit] See also

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

[edit] External Links

• Online Trifid Encipherer/Decipherer

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