Trifid Ciphers

Trifid ciphers are examples of combination ciphers: The encryption process consists of a sequence of several different techniques. In this case substitution followed by fractionation and transposition are used in the encryption. The trifid cipher was invented by amateur cryptographer F´elix Delastelle, ca. 1900.

The encryption key for a trifid cipher consists of a positive integer (the period) and a 3×3×3 array containing all of the distinct letters of the English alphabet plus one additional character. Typically, the additional character in the array is a symbol, such as a dot. The arrangement of the characters in the key array can be chosen at random. Below is the 3D example of an encryption key:

A more basic way of looking at the above graph in a 2D form is by looking at the 3 layers, bottom to top, then numbering them from 1 to 3. Compare the 3D graph to the layers below.

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

Suppose we want to encrypt the message “trick or treat” using a trifid cipher with encryption key consisting of period 4 and the above layers.

i. Represent the letters in our message “trick or treat” with their coordinates in the encryption array: T R I C K O R T R E A T 333 232 221 331 213 122 232 333 232 312 223 333

Layer Row Column How to describe the position Number Number Number of the letter K on the chart.

ii. Now arrange these coordinates in columns and separate the columns into groups of 4 (since the period is defined as 4).

3 2 2 3 2 1 2 3 2 3 2 3 3 3 1 3 1 2 3 3 3 1 2 3 3 2 2 1 3 2 2 3 2 2 3 3 This is the position of K written vertically

iii. Concatenate the rows of each group successively – match the pattern from part ii with what you see below:

3223 3313 3221 2123 1233 3223 2323 3123 2233

iv. Finally, taking the digits in the string from step iii in groups of 3,

322 333 133 221 212 312 333 223 232 331 232 233

use the key array to replace each group with its corresponding character to obtain the ciphertext – go back to the charts and note that “322” corresponds to “P” in the chart from layer 2: P T B I L E T A R C R W Notice that at the end of step i, essentially, we have the result of a substitution cipher. However, instead of replacing each single character with a single symbol, it is replaced by 3 digits. In the subsequent steps these digits are separated and mixed with the digits obtained from other plaintext characters (fractionation and transposition).

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

The following ciphertext was produced using a trifid cipher with period 4 and the above encryption array. B O Y C W C D H B G Q E G A J X

See if you can decrypt it (Answer: Yay Spring Break)

Separately, substitution and transposition ciphers have obvious vulnerabilities. When both are combined with fractionation, as in the trifid cipher, these vulnerabilities are lessened considerably. However, crypt-analysis of the trifid cipher is sufficiently effective so that its use for sensitive messages is ill-advised.

Even though implementation is easy, (it can be done with pencil and paper), and security is better than many other pencil and paper ciphers, practical use of the trifid cipher has been infrequent. It is significant as a link between the classical and the modern: Many present-day encryption procedures, (e.g. AES), consist of more complicated, machine-implemented combinations of substitution, fractionation, and transposition.