Breaking Syllabary Square Codes

• Breaking Syllabary Square Codes - Known Square, Unknown Coordinates
• Problems to Solve - Known Square
• Breaking Unknown Squares
• Problems to Solve - Unknown Square

ONX DE KT5 =
280830 NOV GR 50 =
43341 50055 72248 73940 80688 11600 95638 79752 35913 68764
35538 01252 35869 25528 37384 00095 52445 59038 94170 87373
54962 15526 48529 25528 35184 00095 52445 59318 94730 11954
08237 80078 52806 43464 44385 21639 55592 84177 78097 44790 
16897 14711 18744 76387 99876 42806 39477 87735 55021 24545 =

HJP DE ONX =
280941 NOV GR 42 =
16896 73878 93276 42405 34872 80038 32808 76387 35448 78751
47746 08016 47853 88978 18925 52857 35352 81571 52445 59038 
94172 37696 76925 52899 52907 05158 30709 55590 38177 93851 
00116 38735 00155 27551 00714 46052 20649 75180 83516 87141 
52358 64545 =

5XY DE ONX =
281503 NOV GR 39 =
43682 81616 81160 09114 94889 32764 24056 38751 00714 46052
20649 75186 71511 61815 44358 64600 51516 42850 71605 58789
26479 25521 81379 78893 27642 40578 44380 99987 64280 62832
64863 53500 91505 92841 63879 75180 83519 33946 52454 =

How would we go about breaking it?

Usually we are helped by frequency analysis when breaking ciphers - and even codes - but the use of syllabary squares will thwart the use of any ordinary frequency charts.
When we know the syllabary square used, we could perform a series of test-encryptions with known key coordinates, and calculate a frequency chart showing how often the cells in the syllabary square are used, and even which rows and columns are the most (or least) commonly used.

Doing this for the square above (I have used but a few messages, so it won't be perfect!), will show that all the high frequency cells are single letters (not very surprising), but that the most common English letter, E, is not among them!

Syllabary square with frequencies for the individual cells, as well as for individual rows and columns.

As can be seen in the above picture, the most common cell in the square is hh, plaintext "S", with a frequency of 26. Next comes cell gi, with - a bit surprising perhaps - plaintext "P", having a frequency of 25.

Column g is the least used (frequency = 37), and column h is used the most (frequency = 79).

Rows c and i are used the least, and the most used rows are f and g.

Now let's compare this with the frequency of our cryptogram. It looks like this:

Cipher-row 5 looks promising with three high frequency cells (51, 52 and 55). It is also the most common cipher-row, with a row-frequency of 49. This fits nicely with plaintext-row f, which is the most common plaintext-row, and also has got three high frequency cells containing the letters L, M and N. Cipher-column 5 is one of the two most common columns, and the most common plaintext-column is h. If we make the match, this would make 55 mean M, and two rows below M in the plaintext square, we find another high frequency cell, hh, containing S. We can match this with cipher square 35, which is also of high frequency, so cipher-row 3 is probably equal to plaintext-row h.
On this cipher-row is another high frequency cell, 38 which we can fit against plaintext letter R in cell ha, so cipher-column 8 must be plaintext-column a.
In this column we also find the single - of high frequency - plaintext letters A and D. These are probably represented by ciphers 28 and 78 (or perhaps 18). Since cipher-row 2 doesn't have any more high frequency cells, but cipher-row 7 does (71) and we need an additional high frequency cell for plaintext-row c to fit both plaintext D and E, cipher-row 7 must be plaintext-row c, and it follows that cipher-row 2 must be plaintext-row a.

Plaintext N is in a low-frequency column in the plaintext square, and plaintext L is in a column having a medium frequency, so cipher 52 is a likely candidate for plaintext N, and thus cipher 51 must be plaintext L.

The lowest plaintext column is g, and a safe guess is that this is the least common cipher-column 9.

Let's enter the values found so far into the syllabary square:

And fill in the values we have assumed in the cryptograms (which we have rewritten into two-figure groups) to see what it yields:

Unfortunately there are no obvious fragments of plaintext we can expand. But looking a little deeper will reveal that plaintext MA is always preceeded by cipher 92. We know that the plaintext value must be in column j (to which we have assigned 2 as column key), and that it will have to be com, H, it, Q, thr or Z (since we have assigned row-coordinates to the other values in column j).
The only plausible plaintext is COMMA (it's not likely ITMA would appear four times in so few messages).

In the second message, row two, we now have the plaintext COMMA 57 SSA 15 EN 44 M 90 R. Cipher 57 can be J, 0, K - all impossible - or la or me...
Cipher 15 can be ce, G, ion, P, thi or Y, and toying around with these values will eventually lead to COMMA MESSAGE NUMBER.

Filling in these new values in the syllabary square and decrypting the rest of the messages will leave very little to figure out:

Most coordinates are now assigned a place in the syllable square, and even if obvious plaintext fragments wouldn't suggest themselves in the above messages, the remaining coordinates are few enough to allow us to try all permutations.

The rest of the problem is left to the reader to finish.

An alternate route to solution

When we are given plaintext cribs, or know something about the organization behind the messages, so we are able to make educated guesses at likely plaintext words, there is an alternate route we can take. There are limited ways to encrypt a given plaintext expression, and some of them we can exploit through the inherent pattern, when we know the square used.

The word MESSAGE for instance, can only be encrypted in two different ways, if the legitimate users strive to use as few code groups as possible:

ME	S	S	A	G	E
fi	hh	hh	aa	dh	ce
	Repeated			Last figure
	groups			shared with
				groups 2 and 3

or

M	ES	S	A	G	E
fh	dd	hh	aa	dh	ce
		Last figure		First figure
		shared with		shared with
		first and fifth		second group
		groups

We can compute such instances for given cribs and/or likely plaintext, and look for matches in the cryptograms, and thus make an entry.

The next day, the following cryptograms are intercepted on an enemy radio link, believed to be the same as the one above. Clearly the reconstructed coordinates won't let us read the new traffic - the keys have changed. Your task is to find out the new key.

TOP DE VBY =
290800 NOV GR 40 =
01594 79463 84306 65778 91285 19225 95672 18275 82832 54998
42848 43066 54380 03986 00664 44492 26882 89830 30421 40849
37927 53766 42859 56598 18890 59020 77014 78373 00929 11045 
45218 29225 12154 95775 89056 67621 82524 48014 44517 30049 =

CZ3 DE VBY =
290805 NOV GR 40 =
01594 79463 84306 65778 55885 19225 95672 18275 82832 54998
42848 43066 54380 03986 00664 44492 26882 89830 30421 40849
37927 53766 42859 56598 18890 59020 77014 78373 00929 11045 
45218 29225 12154 95775 89056 67621 82524 48014 44517 30049 =

3F6 DE VBY =
290810 NOV GR 41 =
01594 79463 84306 65778 50781 85192 25956 72182 75828 32549
98428 48430 66543 80039 86006 64444 92268 82898 30304 21408
49379 27537 66428 59565 98188 90590 20770 14783 73009 29110
45452 18292 25121 54957 75890 56676 21825 24480 14445 17300
49070 =

VBY DE 3F6 =
291037 NOV GR 22 =
01524 48681 44517 30049 30734 75382 25986 05378 77802 88682
66006 64444 92251 21801 47837 30077 28983 03042 14084 93747
02724 43007 =

VBY DE TOP =
291043 NOV GR 29 =
01753 76647 19953 91318 89059 02077 21824 46614 05264 99625
47664 44378 00664 44492 26880 14783 73007 72898 30304 21408 
49372 18277 66378 11853 82259 86073 02164 97747 69390 =

VBY DE CZ3 =
291125 NOV GR 20 =
30837 83747 25398 97721 82030 06644 44728 84425 47802 59837 
05012 89830 30421 40849 37014 78373 00218 25482 25987 90149 =

When the square used is unknown, the problem is much harder. To successfully break such a problem, we need a good supply of cryptograms on which to work, and knowledge of what type of plaintext - stereotyped messages, signatures etc. - we can expect is of high importance if we are to get results.

Using nearly identical sequences

One general method to attack this kind of cipher is to look for nearly identical sequences in the cryptograms, with the idea that such sequences might represent the same plaintext, enciphered slightly different.
Let's say we have found these nearly identical sequences in some cryptograms known to be enciphered with a syllabary square (and that we somehow know the word boundaries, so we can be confident they all represent a single word):

A: 14 78 51 33 04
   
B: 14 78 51 33 30 84
   
C: 17 49 78 51 38 40
   
D: 14 78 51 38 49 04
   
E: 14 78 51 38 43 84
   
F: 17 49 78 51 38 43 84
   
G: 17 49 78 51 38 49 30 84
   

If we reformat these sequences, putting equal groups in columns of their own, we will be able to see more clearly what's behind them:

If we assume that variant G - the longest sequence - represents a letter-for-letter encipherment, then apparently the group 43 of variant F represents a digraph, which can also be enciphered as 49 30, and the last group of variant C - 40 - must represent a trigraph, ending with the same letter as 84 represents, and so on.

With enough material, and luck, we might be able to reduce one or several messages into a monalphabetic encipherment, from which we could gradually reconstruct an unknown syllabary square.

Looking for groups with an odd behaviour

• Some syllabary square systems are expanded with additional meanings to each cell. For instance, a common word and/or expression could be added to the lower part of a cell to give it an upper and lower case meaning. The users would need some cells to have the meanings Switch to lower case and Switch to upper case, or similar, to be able to decide what meaning is intended.
  Switching back and forth between lower and upper case meanings in a message, will make such groups stand out in the cryptogram, replacing each other at varying distances as need dictates. Further, if no variants for the switch groups are provided, their frequencies will also be high.

• Groups standing for numbers will also show an odd behaviour. They will often appear in clusters, tabulated data might be numbered in ascending order, leading to easy recovery of the individual figures, and so on.
  Where no variants are provided for the individual figures in a square, the code groups for the figures 1 and 0 will in most cases be of very high frequency, and 0 will often be doubled or even tripled, and thus easily spotted.

• The square could have cells containing punctuation etc., and such groups would also show an odd behaviour.
  Perhaps Period might be identified because its group is frequently found at the end of the cryptograms?

• A cell used to indicate word boundaries would show up having an insanely high frequency.

Reducing different key-date cryptograms to a common key

If we don't have very much material in a certain key, it is sometimes possible to reduce material encrypted with different keys, but the same square, to a common key.
For instance, on a certain key-date, 12 is found to have the highest frequency, and 10 has the lowest frequency. On another key-date 34 is of the highest frequency, and 31 the lowest. There is a high probability that row 1 on the first key-date has become row 3 on the second key-date (we have two things pointing to this fact); column 2 from the first key-date has probably become column 4, and column 0 has become 1 (the evidence for these matches being slightly less certain, but still probable).
We may further find, that what apparently is a signature (or a certain - at this time unknown - word) at the end of messages from a certain sender, is also present in messages from another key-date, giving us a one-to-one match.

We suspect these sequences represents the same name (or word), since we've found it at the end of some cryptograms, and there are several corresponding figures; the beginning 4's of groups one and four of key-date 1 are both 0's on key-date 2, the 3's are 6's, and so on, leading us to the following "skeleton-key":

If we are lucky, we might find out exactly how to change one key-date into the other, and thus be able to extend the material on which to work by re-encrypting one key-date cryptograms into the other key-date.

J6N DE 6D4 =
290710 NOV GR 47 =
00511 26738 21677 28578 37901 36770 85149 19693 18515 01498
65682 69236 30702 19473 93378 48563 55373 66338 37552 26570
85480 58339 44863 71212 63779 32868 24988 59408 48901 77418
11916 05185 63502 13921 72378 29455 55674 70133 62259 99930
12673 82672 85128 80993 48733 78455 73480 =

VBY DE DLF =
290806 NOV GR 23 =
00518 57821 85147 88505 09422 05536 30833 95168 24986 41154 
52200 32107 68852 76705 05940 84890 85170 11811 91650 93012 
38218 55514 21210 =

J6N DE PWP =
290915 NOV GR 98 =
28856 54070 23903 10545 09305 45220 15278 58339 85967 31585 
69569 01594 32558 50051 85413 92290 85921 58704 64215 58512 
67913 86097 19536 05121 55856 79885 41378 41519 84413 78567 
54852 88568 24988 56923 97098 38555 16373 77885 14825 08517 
62018 55014 98858 41515 73853 18518 11916 05130 84158 54486 
85600 48572 85123 62161 21858 44829 85413 72106 55857 28583 
39518 59548 42416 53782 41373 71385 65878 52909 15856 91585
93378 58161 64124 80330 38706 75085 54387 88385 63855 53737 
93856 33837 55226 57085 84492 90985 29718 57185 38375 52265
70302 24293 07851 26738 26728 59176 16159 73000 =

PWP DE DLF =
291145 NOV GR 32 =
54050 95990 28833 95185 91035 56747 93209 16051 01331 76262 
62308 41544 86859 33785 72053 49623 36853 60540 15495 48554 
42691 37242 83378 25452 20152 73022 42951 38512 67382 67285
55142 12130 =

6D4 DE DLF =
291233 NOV GR 56 =
28859 13728 51383 73778 19016 21727 85544 24894 32308 41585
75127 38514 91384 06877 93318 50520 06149 35520 91382 33619 
00519 11701 66384 41900 51291 59136 29318 53712 28605 11913
20158 52971 49671 35220 69245 15517 99933 78691 60513 03870 
67505 52065 91762 97154 38342 16355 37366 33837 55226 57030
22429 51385 92158 70464 21850 02709 =

6D4 DE J6N =
291355 NOV GR 42 =
05348 51267 38267 28512 88099 34873 37845 57348 85199 80985
05485 12785 65682 67877 93307 28554 38788 32883 39519 10355
67479 32091 65090 18062 58176 23048 85844 89785 68249 82915
17741 30215 91650 99408 72423 02242 95138 51267 38267 28578
36421 36615 =

6WI DE DLF =
291418 NOV GR 31 =
28561 37754 38674 85155 41373 81946 46462 24293 66544 24894 
32303 87810 50855 09872 43273 48331 85215 69355 91762 45155 
85543 86748 54137 52733 91362 95530 50514 76732 85439 85916 
55360 =

DLF DE 5XY =
291500 NOV GR 67 =
15890 91248 50855 22037 24857 83712 20278 52093 52203 72485
84631 26959 07378 78563 38759 39513 85681 36784 93013 39337 
86916 05130 91201 68166 20676 57015 89355 90411 84634 26772 
07856 58714 91912 09345 68779 35512 39781 38593 37218 56029 
34394 24178 83158 90912 71071 96385 81697 72055 15522 04838 
94328 56798 35515 53693 06441 38593 37218 56959 86137 22394 
30921 58704 67321 47836 06857 90473 72550 =

3XS DE YEY =
300700 NOV GR 64 =
05730 46488 31735 76465 87446 16161 49451 93059 73598 57323 
72435 29726 28734 69363 92730 57362 15457 37765 02735 12810 
73071 90678 43732 78686 09886 33510 88537 31448 17345 76465 
87447 36230 28540 93207 56534 94256 73472 81432 78738 18873 
66405 34511 31657 59073 30930 69273 71682 41973 36246 52544 
73789 80756 28307 84973 04648 89073 84237 09730 44732 71541 
91730 65776 47735 84356 =

DW6 DE 1KD =
301005 NOV GR 24 =
78425 68698 53306 08809 86395 69655 96346 13473 88400 67341 
93692 34945 15295 97357 06518 85386 11492 43045 01147 32475 
23568 86518 40775 31865 =

DW6 DE JM6 =
301122 NOV GR 77 =
57932 35788 26784 07487 53533 06088 09863 39296 82347 93482 
49325 18923 87445 37309 85927 73078 73385 75409 98072 84927 
85650 84153 15404 01845 58861 61464 05677 15340 87026 58909 
45308 55609 88881 46473 33787 32385 46252 68639 56497 76580 
14995 68678 42467 34558 64569 85337 28259 31411 23283 52373
38534 04138 45405 30433 19494 35653 41831 53085 23540 96545 
87442 43739 73455 82474 90731 47353 09939 36365 97068 80986 
39565 34904 64832 82715 41917 33358 77880 =

DW6 DE PPE =
301130 NOV GR 61 =
07005 37377 65028 37773 32088 09278 73536 28022 38378 84288 
24901 44256 86985 33060 88098 63392 20962 06134 34776 58067 
71053 97345 40004 54190 73351 52900 73307 72323 18733 08524 
37738 84006 73011 82345 13264 11725 26863 39238 45138 88328 
49772 37330 45401 54064 65752 37399 56377 81424 41718 86537 
26243 00959 28337 80216 49228 59255 82203 20880 92785 76465
87440 =

DW6 DE KT5 =
301207 NOV GR 25 =
65776 91535 07855 30193 93872 30889 20962 89423 86339 23847 
28929 01478 40748 75353 30609 67934 03344 84984 23709 73706 
27154 19173 93926 40953 41490 =

DW6 DE 3XS =
301705 NOV GR 38 =
57937 37842 56967 92017 20034 95606 20349 62255 57453 06557
28222 05324 51454 32849 56062 03461 22612 23449 56069 63434 
22202 23449 56069 69634 22962 29649 56069 61734 22342 22049 
56066 13461 22822 23449 24304 50114 73688 08188 =

VYP DE NS1 =
010710 DEC GR 90 =
16360 85787 51493 73421 91515 35896 84747 24893 62580 71063 
14230 13058 10518 11613 51810 95437 59765 88189 50132 35948 
58961 83501 53759 90181 59491 64797 94145 31366 13514 18981 
76390 32881 36085 78722 21084 41351 59443 66988 81705 18162  
46810 13501 53620 97762 56071 06219 20044 49075 63881 00081 
77818 97719 04594 67572 48013 02997 96415 86245 92946 88132 
57578 72235 62481 04461 23348 13257 57687 24801 89934 83314 
17568 11944 31051 48728 99852 16576 29607 63289 86233 25697 
09285 43796 97055 63017 97415 88157 62361 57781 61294 11414 =

BRS DE NAW =
010733 DEC GR 102 =
77093 67688 16883 28709 07105 11277 49010 16292 48104 46123 
24676 71167 67305 94801 57033 61401 81943 23153 36621 07653 
00048 49151 48104 46004 24955 24338 24068 10974 48235 38990  
47624 45301 23849 15148 10446 00424 95430 61124 67819 73276 
58125 17753 71485 45300 04849 65448 10446 12324 79676 76738 
11814 51413 51890 15358 69962 55301 23849 65448 10446 12324 
43804 33867 52624 68101 98422 35344 96556 22553 00048 49151 
48104 46004 24248 08095 11435 38996 42608 16817 97482 28833 
04534 65243 56544 46123 16937 63633 14899 61381 05587 21970 
14883 15944 44104 89166 72480 13017 97482 28157 36148 11208
44612 39730 =