Digrafid

History

First published in the Sep-Oct 1960 edition of American Cryptogram Association (ACA) magazine The Cryptogram the Digrafid cipher is a fractionated cipher developed by ACA member KNUTE. It is a combination of the Bifid and Trifid cipher but uses two keyed alphabets which include the # symbol to form 27-letter alphabets.

Description

Encipherment is performed by dividing the plaintext into digraphs which are grouped into a period length. Each letter pair is replaced by three numbers derived from its position in the alphabets then replaced. These numbers are then fractionated and used to produce two cipher text letters. To encipher text using the Digrafid cipher two keyed alphabets are created from key words, with repeated letters being omitted, followed by the unused letters of the alphabet in alphabetic order. These are appended with the # symbol to form two 27-letter alphabets. If required the # symbol can be inserted at any position in the alphabets. For example the key word GOLF is appended with unused alphabet letters and the # symbol to produce the keyed alphabet:

GOLFABCDEHIJKMNPQRSTUVWXYZ#

and the key word CLUB is appended with unused alphabet letters and the # symbol to produce the keyed alphabet:

CLUBADEFGHIJKMNOPQRSTVWXYZ#

The keyed alphabets are written into a table; one horizontally to form a 3x9 grid and the other vertically to form a 9x3 grid both touching at one corner. Columns of the first keyed alphabet, the rows of the second keyed alphabet and the intersection of these are numbered 1-9 as shown in the following table:

1 2 3 4 5 6 7 8 9

G O L F A B C D E 1 2 3

H I J K M N P Q R 4 5 6

S T U V W X Y Z # 7 8 9

C H R 1

L I S 2

U J T 3

B K V 4

A M W 5

D N X 6

E O Y 7

F P Z 8

G Q # 9

The plaintext is then divided into pairs and in period length groups. If the plaintext contains an odd number of letters a null letter, such as X, is added at the end of the text to complete the last letter pair. The first letter of each pair is located in the top table and the second letter in the bottom table. A 3-digit number is produced using the column number of the first letter in the top table, the number at the intersection of the two letters and the row number of the second letter in the bottom table. These three numbers are written vertically below the first letter pair. For example with the letter pair GO and using the above table G is in column 1 in the first table, O is in row 7 of the bottom table and the number at the intersection of the two letters is 2. The numbers 1 2 7 are written below the letter pair GO. Using the following Mark Twain quote as an example "Golf: A good walk ruined." and continuing for the remainder of the plaintext produces the table:

GO LF AG OO DW AL KR UI NE DX

1 3 5 2 8 5 4 3 6 8

2 1 1 2 3 1 6 8 4 3

7 8 9 7 5 2 1 2 7 6

These digits are then read horizontally within each group and replaced by the letter represented by the numbers in the table to produce the ciphertext. For example the first number group 1 3 5 and using the above table the letter in the top table the letter at the intersection of 1 and 3 is G and the letter in the bottom table at the intersection of 3 and 5 is W producing the first ciphertext group GW. Continue with the next next numbers in the same group 2 1 1 producing the next ciphertext group OC. Continuing for the remainder of the number groups produces the ciphertext.

Example

Keyword #1: GOLF

Keyword #2: CLUB

Period: 6

Plaintext: Golf: A good walk ruined.

123456789

GOLFABCDE 123

HIJKMNPQR 456

STUVWXYZ# 789

CHR 1

LIS 2

UJT 3

BKV 4

AMW 5

DNX 6

EOY 7

FPZ 8

GQ# 9

go lf ag oo dw al kr ui ne dx

1 3 5 2 8 5 4 3 6 8

2 1 1 2 3 1 6 8 4 3

7 8 9 7 5 2 1 2 7 6

GW OC YQ TM OR PI FX XK GO DX

Plaintext: golfag oodwal kruine dx

Ciphertext: GWOCYQ TMORPI FXXKGO DX

Solving

Solving method: Hill Climbing.