Periodic Gromark

History

The Gronsfeld with Mixed Alphabet and Running Key or Gromark cipher first appeared in the American Cryptogram Association (ACA) Mar-Apr 1969 edition of the ACA's magazine The Cryptogram and was developed by ACA member DUMBO. The Gromark was based on the Gronsfeld cipher which was invented by the Bavarian Field Marshal Count Jobst Maximilian von Gronsfeld (1598-1662) and based on the Vigenère cipher. Four years later DUMBO developed a variation of the Gromark called the Periodic Gromark cipher and described its construction in the Mar-Apr 1973 edition of The Cryptogram. This variation adds a further step in the enciphering process to make it more difficult to solve without the keys.

Description

To encipher text using the Periodic Gromark cipher choose a keyword and from it create a keyword mixed alphabet. This is produced by creating a keyed alphabet from the keyword with repeated letters being omitted and followed by the unused letters of the alphabet in alphabetic order. This is then written into a transposition block with the number of letters in the keyword determining the number of columns in the block. For example appending unused alphabet letters to the key word WRIGHT produces the keyed alphabet WRIGHTABCDEFKLMNOPQSUVXYZ. Writing this into a transposition block gives:

6 4 3 1 2 5

W R I G H T

A B C D E F

J K L M N O

P Q S U V X

Y Z

Finally the letters in each column are taken off the block in alphabetical order to produce the mixed keyed alphabet. Using the above table this produces the key GDMU HENV ICLS RBKQZ TFOX WAJPY or GDMUHENVICLSRBKQZTFOXWAJPY.

Straight alphabet: abcdefghijklmnopqrstuvwxyz

Keyed alphabet: GDMUHENVICLSRBKQZTFOXWAJPY

The alphabetical order of the keyword is used to create a running numerical key by adding successive pairs of digits, subtracting 10 if the total is greater than 9, and appending the result to the end of the running key. This is repeated until its length is the same as the plaintext. So using the keyword WRIGHT produces the primer 643125 adding the 1st number, 6 to the 2nd number, 4 gives 6+4=10. Subtracting 10 gives 0 and the running key becomes 6431250. Then the 2nd number, 4 is added to the 3rd number, 3 to give 4+3=7 gives 7 and the running key becomes 64312507. This continues to the same length as the plaintext producing the running key 64312507437571702288724065964614500759507244579689265471819189900978909657.

Running key: 64312507437571702288724065964614500759507244579689265471819189900978909657

Plaintext: adoctorcanburyhismistakesbutanarchitectcanonlyadvisehisclientstoplantvines

The plaintext is divided into groups of keyword length and letters of each keyword are written above each plaintext group one letter at a time repeating as required to the end of the cipher. E.g. W over the 1st group, R over the 2nd group and so on. These letters will determine the slide position of the keyed alphabet or alphabetic shift for each letter group. Each cipher text letter is determined by both the numerical key and the group key.

Added key: W R I G H T W R ...

Key: 643125 074375 717022 887240 659646 145007 595072 445796 ...

Plaintext: adocto rcanbu ryhism istake sbutan archit ectcan onlyad ...

Encryption is carried out by shifting the keyed alphabet so that plaintext letter a is located above the group letter. For the first group the following keyed alphabet is used:

Straight alphabet: abcdefghijklmnopqrstuvwxyz

Keyed alphabet: WAJPYGDMUHENVICLSRBKQZTFOX

Taking the 1st plaintext letter a and running key number above it, 6 locate the plaintext letter in the straight alphabet and count 6 places to the right reaching g. Below this in the keyed alphabet is the 1st ciphertext letter D. Next the 2nd plaintext letter is d and counting right 4 places, the 2nd running key number, is plaintext h. Below this in the keyed alphabet is the 2nd ciphertext letter M and so on. When the group is complete the keyed alphabet is shifted again with the letter R placed below the straight alphabet letter a. Completing the process results in the following ciphertext:

Ciphertext: DMRPZKUWZMXSNVAZMAZGGMKHMLVUIJFRPPYTHNOJMLHUMTWWSYMFXXYUOCBKEENFOPPRORILHX

Example

Keyword: WRIGHT (643125)

Encipher the following Frank Lloyd Wright quote "A doctor can bury his mistakes but an architect can only advise his clients to plant vines.”

Added key: W R I G H T W R I G H T W

Key: 643125 074375 717022 887240 659646 145007 595072 445796 892654 718191 899009 789096 57

Plaintext: adocto rcanbu ryhism istake sbutan archit ectcan onlyad visehi sclien tstopl antvin es

Ciphertext: DMRPZK UWZMXS NVAZMA ZGGMKH MLVUIJ FRPPYT HNOJML HUMTWW SYMFXX YUOCBK EENFOP PRORIL HX

Solving

Solving methods: Hill Climbing and Dictionary keyword search.

After selecting the Gromark cipher, the Key primer must be entered in the Cipher Settings ribbon group. The length of the primer will determine the key period.