Gromark Tutorial

The Gromark is similar to the Ragbaby in that a different shift is used at each position to encipher from plain to cipher text. The major differences are:

  1. The Gromark shift for each letter is calculated from a 5 digit primer from which a running key is formed by addition of successive pairs of digits and dropping tens. The Ragbaby shift is found from the position of the letter in the plain text (Both word and letter position).
  2. The Ragbaby has a single alphabet for both plain and cipher text. The Gromark has independent plain and cipher alphabets positioned over one another. However, the Gromark plain alphabet is always in standard form (i.e., abcde…xyz).

As with the Ragbaby, the major problem with solution of a Gromark is placing the crib in the cipher text. This placement provides a start on determining the Cipher alphabet.

Using JA03 E-06 as an example (And assuming you can do the running key arithmetic), we start with:

Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: **************************
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
***** ***** ***** ***** ***** ***** ***** ***** ***** ***** *****

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
***** ***** ***** ***** ***** ***** ***** ***** ***** ***** *

The crib is the word ‘college’.

Unlike the Ragbaby, the Gromark has no simple way to place the crib. All positions are equally likely and each needs to be evaluated. This is done for each position as follows:

  1. The plaintext letters in the crib each have a unique position in the plaintext alphabet. List out these values. For ‘college’, these values are: c=3, o=15, l=12, l=12, e=5, g=7, e=5.
  2. For each position in the cipher text, calculate the position of the cipher letter in the cipher alphabet by adding the plaintext letter position to the positions shift value. Consider the following examples:
Position 1
pt:  c  o  l  l  e  g  e
p#:  03 15 12 12 05 07 05
sh:   6  4  3  1  7  0  7
C#:  09 19 15 13 12 07 12
CT:  J  H  O  I  B  C  K

Position 32
pt:  c  o  l  l  e  g  e
p#:  03 15 12 12 05 07 05
sh:   3  1  8  1  0  4  9 
C#:  06 16 20 13 05 11 14
CT:  L  S  A  L  B  C  S
 
Position 35
pt:  c  o  l  l  e  g  e
p#:  03 15 12 12 05 07 05
sh:   1  0  4  9  9  1  4
C#:  04 15 16 21 14 08 09
CT:  L  B  C  S  R  G  O

Position 62
pt:  c  o  l  l  e  g  e
p#:  03 15 12 12 05 07 05
sh:   2  7  4  6  1  9  1
C#:  05 22 16 18 06 16 06
CT:  E  X  N  O  W  N  W 
  1. Each position is evaluated and placed into one of the following three classifications:
    1. Inconsistent: The position is inconsistent with the placement of the plain text. This can happen for one of two reasons. In the first case, the same cipher alphabet position is shown to have two different cipher letters. Position 1 is an example of this category (i.e., CT position 12 has both B and K assigned to it). In the second case, the same cipher letter has two different cipher alphabet positions assigned to it. Position 32 is an example of this (i.e., CT letter S is assigned positions 14 and 16).
    2. Neutral: This position is not inconsistent with the placement of the plain text. This is due to the fact that all the cipher text letters at that position are different and so are all the calculated cipher letter positions. Position 35 is an example of this category (i.e., No identical cipher text letters and no identical calculated cipher alphabet positions). This position must remain a candidate for placement of the cipher text, but the evidence is weak.
    3. Consistent: This position is consistent with placement of the cipher text. Repeated cipher text letter all have the same calculated cipher alphabet positions with no other inconsistencies. Position 62 is an example of this category (i.e., The cipher text letters N and W are repeated and have the same positions values in both cases (16 and 6 respectively)). Because the probability of such coincidences is low, this type of position is a far more likely placement for the crib than a ‘not inconsistent’ position.

For the example here, the total number of positions in each category breaks down as follows:

Inconsistent:  82
Neutral: 16
Consistent: 02

Of the two consistent positions (62 and 99), No. 62 has two consistencies while No. 99 has only one. Therefore, the first guess for the position of ‘college’ is at position No. 62.

From the evaluation of position 62 we get the following cipher alphabet positions:

E = 05, X = 22, N = 16, O= 18, W = 06.

This provides us with:

Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: ****EW*********N*O***X****
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
**o** ***** ****n *o**d e**** ***** ***** ***** n*he* ****d ****e

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
***** *coll ege** ****i ***n* ***** ***v* ***** **v*n ***** *

The string of cipher text around position 42 suggests the plain text ‘the’. Based on this, we can find the position of the cipher text letter T. The pt position of ‘t’ is 20. The Shift at position 42 is 3. Therefore, ‘T’ is at position CT = 20 + 3 = 23.

This provides:

Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: ****EW*********N*O***XT***
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
**o** ***** ****n *o*nd e**** ***s* ***** ***** nthe* ****d ****e

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
***** *coll ege** w***i ***n* ***** ***v* ****n **v*n ***** *

The string we just modified now suggest the phrase ‘in the’ or ‘on the’. Trying the first option, we can find the position of cipher text letter G. The pt position of ‘i’ is 09. The Shift at position 40 is 1. Therefore, ‘G’ is at position CT = 09 + 1 = 10.

This provides:

Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: ****EW***G*****N*O***XT***
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
**o** ***** ****n *o*nd e**** ***s* ***** ****i nthe* *i*ed ****e

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
***** *coll ege** w***i ***n* *a*** ***v* ****n **v*n ***** *

The string starting at position 16 suggests the word ‘founded’. This will provide:

The pt position of ‘f’ is 06. The Shift at position 16 is 8. Therefore, ‘I’ is at position CT = 06 + 8 = 14.

The pt position of ‘u’ is 21. The Shift at position 18 is 7. Therefore, ‘Q’ is at position CT = 21 + 7 = 28 = 2 (Mod 26).

The pt position of ‘d’ is 04. The Shift at position 22 is 0. Therefore, ‘L’ is at position CT = 04 + 0 = 4.

This provides:

  • Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: *Q*LEW***G***I*N*O***XT***
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
**om* ***f* ****n found ed*** ***s* *a**c ****i nthe* *ited **a*e

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
***** ecoll ege** w***i *m*n* ma*** n**v* ****n **v*n *y*** *

The string starting at position 45 suggests the words ‘United States’. This will provide:

  • The pt position of ‘u’ is 21. The Shift at position 45 is 5. Therefore, ‘J’ is at position CT = 21 + 5 = 26.
  • The pt position of ‘n’ is 14. The Shift at position 46 is 7. Therefore, ‘R’ is at position CT = 14 + 7 = 21.
  • The pt position of ‘s’ is 19. The Shift at position 51 is 8. Therefore, ‘A’ is at position CT = 19 + 8 = 27 = 1 (Mod 26).
  • The pt position of ‘t’ is 20. The Shift at position 52 is 9. Therefore, ‘D’ is at position CT = 20 + 9 = 29 = 3 (Mod 26).

This provides:

Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: AQDLEW***G***I*N*O**RXT**J
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
t*om* ***f* **s*n found edt** ***s* *a*sc ***li ntheu nited state

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
sa*t* ecoll ege** w***i am*n* ma*y* n**v* ****n **v*n ty*** *

The string starting at position 59 suggests the words ‘The College of William and Mary’. This will provide:

  • The pt position of ‘h’ is 08. The Shift at position 60 is 7. Therefore, ‘M’ is at position CT = 08 + 7 = 15.
  • The pt position of ‘f’ is 06. The Shift at position 70 is 7. Therefore, ‘V’ is at position CT = 06 + 7 = 13.
  • The pt position of ‘i’ is 09. The Shift at position 72 is 0. Therefore, ‘Y’ is at position CT = 09 + 0 = 09.
  • The pt position of ‘l’ is 12. The Shift at position 74 is 7. Therefore, ‘C’ is at position CT = 12 + 7 = 19.
  • The pt position of ‘d’ is 04. The Shift at position 80 is 7. Therefore, ‘P’ is at position CT = 04 + 7 = 11.
  • The pt position of ‘r’ is 18. The Shift at position 83 is 2. Therefore, ‘Z’ is at position CT = 18 + 2 = 20.

This provides:

Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: AQDLEW**YGP*VIMN*OCZRXT**J
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
t*om* s*eff *rson found edth* *i*s* la*sc *o*li ntheu nited state

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
satth ecoll egeof willi amand mary* ns*ve n***n *even tynin e

The cipher is now essentially solved. Only 6 cipher text letters remain unplaced. A perusal of the uncovered plain text quickly shows that the text begins with the words ‘Thomas Jefferson’ and ends with the words ‘in seventeen seventy nine’. With this info, the positions of the remaining cipher text letters can be uncovered.

This provides:

Key: 64317
Plain:  abcdefghijklmnopqrstuvwxyz
Cipher: AQDLEWFBYGPHVIMNKOCZRXTSUJ
64317 07487 71254 83792 10613 16744 73181 04991 43805 71852 89370
JHOIB CKYIV HCRZO IOQTW WLJYB FMUTS CLSAL BCSRG OTNEJ RGQGW ADLAE
thoma sjeff erson found edthe first lawsc hooli ntheu nited state

72077 92746 19107 00177 01847 19218 01398 14279 56964 15505 6
JDZAM IEXNO WNWMV TYVCN AIYOP IGZJK IZBEV MSFHT SPEPO RLCYC P
satth ecoll egeof willi amand maryi nseve nteen seven tynin e