GRASP Cipher


A six-layer challenge cipher created by Zackery Belanger to demonstrate solvability.

Update October 2024: The GRASP Cipher was solved manually by Megan Stewart of Flint, Michigan.

-Zackery Belanger
01 September 2024

I believe that Ed Scheidt developed something like this for Kryptos K4. The method allows a key word to be expressed in the ciphertext at each layer, which provides a built-in clue for the next layer, and allows the codemaker to use as many layers as they like. This method demonstrates the feasibility that sequences like KCAR at the end of Kryptos K4 are meaningful and intentional.

The GRASP cipher is as follows:

KXKPXWFTSH?OWPXOVUSUAQBKJQRPGQ

Note that its 30-character length and low index of coincidence (0.03678) make it daunting from a cryptanalysis perspective.

I'll share some important information and demonstrate how Layers 1 and 2 work, and leave the remaining layers to the interested codebreakers.

Important information:

  1. The 27-letter alphabet for this cipher is: OCGXRJLINSHVBTDQAPZK?WEFYUM

  2. The primary key is Longfellow's translation of Dante's Divine Comedy Vol II: Purgatorio; 1870; by Fields, Osgood & Co, Boston. This edition and printing is required, and only the poem is in play (pages 1 - 166). I've made a searchable PDF with all extraneous content removed available here. The cipher would work even with only the print book in hand, but would take a lot more time to solve.

  3. For built-in clue identification, Q and X are wild.

  4. A word unscrambler is helpful; this one accepts wild characters.

  5. The Layer 1 clue is five characters long, and the remaining clues are all four characters long.

  6. Progress always moves forward in Purgatorio for this implementation, never backward.

  7. All clues occur at the end of the ciphertext.

Layer 1:

KXKPXWFTSH?OWPXOVUSUAQBKJQRPGQ

Inspect the last five characters of the ciphertext, and remember Q and X are wild. These characters can be unscrambled to make four words that occur in Purgatorio: PURGE (p 1, 3, 22, 128, 138), GRASP (p 2, 24), GRAPE (p 16), and GROUP (p 145).

Try the first occurrence of GRASP, which is on page 2. Take the final 30 characters from the page, and transform the ciphertext by summing characters using the given alphabet (e.g. K=20 and V=12, so K+V=32 which is 5, or R):

KXKPXWFTSH?OWPXOVUSUAQBKJQRPGQ
VERENTHEMADEINMEMYKNEESANDBROW
RMYTBNISSONFGMXFVFGIBVESDXPEXH

The last four characters of the new ciphertext contain the scrambled clue for Layer 2.

Layer 2:

Words that can be made from PEXH that occur in Purgatorio are HOPE (p 12, 15, 16, 26, 39, 65, 84, 93, 101, 152) and HELP (p 51). Neither HOPE p 12 nor p 15 yield anything interesting. The third HOPE works, page 16. Again grab the last 30 characters on the page and transform:

RMYTBNISSONFGMXFVFGIBVESDXPEXH
MASTERSAIDIWHATWAYSHALLWETAKE?
RAIONTPMPQAZTAPZCWBZGZGRHPIQMR

Inspect the last four characters and carry on.

If you are curious, you can try using PURGE, GRAPE, GROUP, and the later occurrence of GRASP in layer 1, and you'll find that none of them lead anywhere. You can also try with four- or six-letter clues if you like; you also won't get anywhere.

In this system false leads occur by chance, but when you're off-path it will usually quickly, always eventually, fall apart.

A carefully chosen alphabet is required for this method. The wild characters need to show up often enough to be useful but not so often as to cause the possible clues to explode in number. How the characters combine to other characters is a delicate balance.

The appearance of a new clue in every layer may make very deep systems possible, especially with a more refined alphabet, additional careful rule relaxations (e.g. V and U could be interchangeable), a mixing in other cipher types (e.g. a careful transposition would re-seed the last four characters), and of course, more books.