You are right with what you’ve said (maybe except the homophone substitution, I do believe in that..why should it be different).

BTW, a nice word, btw, for the third ++ is ‘CALLCENTER’..it not only fits the following ‘w’ symbol but also a third (repeating) symbol very well (six symbols hit repeating letters..). ‘PASSPORT’ is also a nice one.

As Z had used the letter ‘L’ with an above average frequency in the past, to me ‘L’ is an equal candidate to ‘S’. All other symbols I’ rather rule out with a chance of let’s say >90 to 95%.

The run I currently do is focussing on longer words amongst non-outlier bigrams/trigrams with one or two additional pre-conditions: The L and the w symbol to be rather ‘frequent’ (ETAOINSRHDLU). There will be more runs, also with the ‘L’ and is the nice part of it that all of such assumptions can be modified at any time.

A short look on the performance speed: With 185,000 pre-set variables as well as an additional pre-set of one bigram, one letter from A-Z and one frequent letter we currently end up with

185,000 x 28 x 26 x 12 = ~1.616.160.000 or 1.6B

different settings being checked for the first string (all of the above being checked with the algorithm to find any word from the dictionary). The program then continues to add another letter from A-Z as well as another frequent one. Therefore it covers

1.616.160.000 x 26 x 12 = 504.241.920.000 or 504.2B

different settings. All of those have to be checked on the dictionary (thus x5,000, leading us to approx. 2,500 trillion checks of words on different positions/settings).

However, computation effort is less as the program continues to search for the second string only if at least one word has been found in the first string. Still, due to the search in the database (checking all the words at all potential positions in the string..) the computation takes a while and to be honest is close to Freddy Kruger’s Elm Street..

My 2.4Ghz tablet is currently calculating since 2-3 days and will it run most likely until tomorrow or the day after tommorow. Then, however, all possible combinations have been found according to the pre-settings made.

So far, it seems like some 500,000 settings out of 504.2B do have a match with one word being found in each of the strings (those can be re-checked against a third string later ). Many of those 500,000 results actually do show similar conjugations and combinations leading to total of approximately 500 different cleartext combinations. Out of 504B variations only 500 potential cleartext – partial – solutions…and still a step left by checking those results against a third string.

Thus, with the current settings the ‘cracking’ ratio is approximately 1,000,000,000 : 1 meaning that one single potential solution would be found out of one Billion different homophone combinations. With some luck, Z’s homophone setting is amongst those results. If not, different settings have to be set-up.

By checking Billions and Billions of such different settings, the cleartext may (or may not) be found in the future. The biggest ‘enemy’ of such cracking process, however, is if Z had used only short words in at least one of the strings. ‘So she did not have‘ as a partial cleartext, for example, would make the crosschecking amongst the strings to each other harder as the computation is increasing due to a larger dictionary to be used as well as way more results (memory issue again..).

QT

After five days of computation, below are all results out of 504.2B variations (words length >5; two strings; w and L symbol frequent; + symbol ‘S’). Please note that there were 579,456 results, however after duplikates (different conjugations on other positions of the strings) there were only based on 394 different cleartext combinations (at least one word in each string). Some interesting finds, e.g. words such as ‘schools’, ‘shoots’, ‘present’, ‘arrest’, ‘secure’ or ‘release’. Results have not been analysed further, yet.

QT

hereinbehind
sourcechorus
searchechoed
sourcesourcescoasts
softnesscoasts
finestcoasts
honestcoasts
genesiscoasts
resenthideous
presentresenthideous
prestonhideous
resisthideous
resorthideous
stresshideous
afreshhideous
arresthideous
caresshideous
empresshideous
resentwheels
presentresentwheels
resentcheers
presentresentcheers
resentsheets
presentresentsheets
resentcheese
presentresentcheese
prestonwheels
prestoncheers
prestonsheets
prestoncheese
resistwheels
resistcheers
resistsheets
resistcheese
resortwheels
resortcheers
resortsheets
resortcheese
hithercheers
stresswheels
stresscheers
stresssheets
stresscheese
afreshwheels
afreshcheers
afreshsheets
afreshcheese
arrestwheels
arrestcheers
arrestsheets
arrestcheese
afreshhithercheers
retirecheers
retireresentcheers
retireresistcheers
retireresortcheers
retirehithercheers
securecheese
caresswheels
caresscheers
caresssheets
caresscheese
secureresentcheese
secureresistcheese
secureresortcheese
empresswheels
empresscheers
empresssheets
empresscheese
releasefortress
releasemortar
releasemortal
releasevirtuevirtues
releaseparties
peasantfortress
peasantmortar
peasantmortal
peasantvirtuevirtues
peasantparties
seasonfortress
reasonfortress
seasonmortar
seasonmortal
reasonmortar
reasonmortal
seasonvirtuevirtues
reasonvirtuevirtues
seasonparties
reasonparties
seasonseasonsfortress
reasonreasonsfortress
seasonseasonsmortar
seasonseasonsmortal
reasonreasonsmortar
reasonreasonsmortal
seasonseasonsvirtuevirtues
reasonreasonsvirtuevirtues
seasonseasonsparties
reasonreasonsparties
easterfortress
eastermortar
eastermortal
eastervirtuevirtues
easterparties
releasereleasedfortress
ceasedfortress
releasereleasedmortar
releasereleasedmortal
ceasedmortar
ceasedmortal
releasereleasedvirtuevirtues
ceasedvirtuevirtues
releasereleasedparties
ceasedparties
treasonreasonfortress
treasonreasonmortar
treasonreasonmortal
treasonreasonvirtuevirtues
treasonreasonparties
treasonreasonreasonsfortress
treasonreasonreasonsmortar
treasonreasonreasonsmortal
treasonreasonreasonsvirtuevirtues
treasonreasonreasonsparties
peasantbehind
seasonbehind
reasonbehind
seasonseasonsbehind
reasonreasonsbehind
easterbehind
ceasedbehind
peasantbehold
peasantechoed
peasantpeasantsshores
peasantpeasantsashoreshores
peasantchorus
peasantpeasantsshoots
peasantschoolschools
peasantpeasantsshouts
seasonbehold
reasonbehold
seasonechoed
reasonechoed
seasonshores
seasonashoreshores
seasonchorus
reasonshores
reasonashoreshores
reasonchorus
seasonshoots
seasonschoolschools
reasonshoots
reasonschoolschools
seasonshouts
reasonshouts
seasonseasonsbehold
reasonreasonsbehold
seasonseasonsechoed
reasonreasonsechoed
seasonseasonsshores
seasonseasonsashoreshores
seasonseasonschorus
reasonreasonsshores
reasonreasonsashoreshores
reasonreasonschorus
seasonseasonsshoots
seasonseasonsschoolschools
reasonreasonsshoots
reasonreasonsschoolschools
seasonseasonsshouts
reasonreasonsshouts
easterbehold
easterechoed
eastershores
easterashoreshores
easterchorus
eastershoots
easterschoolschools
eastershouts
ceasedbehold
ceasedechoed
ceasedshores
ceasedashoreshores
ceasedchorus
ceasedshoots
ceasedschoolschools
ceasedshouts
finishcoasts
sinistercoasts
prisonhideous
arisenhideous
crisishideous
christhideous
prisonwheels
prisoncheers
prisonsheets
prisoncheese
arisenwheels
arisencheers
arisensheets
arisencheese
crisiswheels
crisischeers
crisissheets
crisischeese
christwheels
christcheers
christsheets
christcheese
reversefortress
reversemortar
reversemortal
reversevirtuevirtues
reverseparties
emersonfortress
personfortress
emersonmortar
emersonmortal
personmortar
personmortal
emersonvirtuevirtues
personvirtuevirtues
emersonparties
personparties
personpersonsfortress
personpersonsmortar
personpersonsmortal
personpersonsvirtuevirtues
personpersonsparties
reverseversesfortress
reverseversesmortar
reverseversesmortal
reverseversesvirtuevirtues
reverseversesparties
persistfortress
persistmortar
persistmortal
persistvirtuevirtues
persistparties
rogersfortress
rogersmortar
rogersmortal
rogersvirtuevirtues
rogersparties
versesfortress
versesmortar
versesmortal
versesvirtuevirtues
versesparties
riversfortress
riversmortar
riversmortal
riversvirtuevirtues
riversparties
riversversesfortress
riversversesmortar
riversversesmortal
riversversesvirtuevirtues
riversversesparties
aversefortress
aversemortar
aversemortal
aversevirtuevirtues
averseparties
averseversesfortress
averseversesmortar
averseversesmortal
averseversesvirtuevirtues
averseversesparties
emersonbehind
personbehind
personpersonsbehind
versesbehind
persistbehind
aversebehind
averseversesbehind
emersonbehold
personbehold
emersonechoed
personechoed
emersonshores
emersonashoreshores
emersonchorus
personshores
personashoreshores
personchorus
emersonshoots
emersonschoolschools
personshoots
personschoolschools
emersonshouts
personshouts
personpersonsbehold
personpersonsechoed
personpersonsshores
personpersonsashoreshores
personpersonschorus
personpersonsshoots
personpersonsschoolschools
personpersonsshouts
versesbehold
versesechoed
versesshores
versesashoreshores
verseschorus
versesshoots
versesschoolschools
versesshouts
persistbehold
persistechoed
persistshores
persistashoreshores
persistchorus
persistshoots
persistschoolschools
persistshouts
aversebehold
averseechoed
averseshores
averseashoreshores
aversechorus
averseshoots
averseschoolschools
averseshouts
averseversesbehold
averseversesechoed
averseversesshores
averseversesashoreshores
averseverseschorus
averseversesshoots
averseversesschoolschools
averseversesshouts
aversesearchechoed
recessfortress
recessmortar
recessmortal
recessvirtuevirtues
recessparties
lesserfortress
lessermortar
lessermortal
lesservirtuevirtues
lesserparties
lessonfortress
lessonmortar
lessonmortal
lessonvirtuevirtues
lessonparties
lessonlessonsfortress
lessonlessonsmortar
lessonlessonsmortal
lessonlessonsvirtuevirtues
lessonlessonsparties
lessenfortress
lessenmortar
lessenmortal
lessenvirtuevirtues
lessenparties
lesserbehind
lessonbehind
lessonlessonsbehind
lessenbehind
lesserbehold
lesserechoed
lessershores
lesserashoreshores
lesserchorus
lessershoots
lesserschoolschools
lessershouts
lessonbehold
lessonechoed
lessonshores
lessonashoreshores
lessonchorus
lessonshoots
lessonschoolschools
lessonshouts
lessonlessonsbehold
lessonlessonsechoed
lessonlessonsshores
lessonlessonsashoreshores
lessonlessonschorus
lessonlessonsshoots
lessonlessonsschoolschools
lessonlessonsshouts
lessenbehold
lessenechoed
lessenshores
lessenashoreshores
lessenchorus
lessenshoots
lessenschoolschools
lessenshouts

How do you interpret those results?

Will you now run a program with the + symbol solved as L?

If I post a partial solution, in a couple days or week or so, when you get some open computer time, could you run it in your system to try to get the computer program to more fully solve the code?

The results I posted are only the cleartext words out of two strings. Thus formatted, however I do know exactly in which pre-setup on which position which word occurs.

Currently I cross-check against a third string, however after one hour only I already see that I’ll get too many results (might have many reasons).

If you give a certain set-up it might be possible to run it..however my prog tries to solve the cipher ‘step by step’ not as an immediat, complete solution. Depending on how many variables are put in, too..if you add 5-6 alphabetical letters its 26^5 which already is too much sort of..anyway, we can try.

To interpret them:

– Number shows which of my 185,000 pre-sets has been used
– The two strings that were analyzed
– Position (‘index’) on which letter of the string the word has been found (starting from zero, not from ‘1’..Python-specific)
– Words that were found

In the example below the set 40922 and 41250 have shown a match. The result list is long, more than half a million hits were found..but less than 400 different sets of words (as listed in the previous post..as you can see the word ‘easter’ shows up multiple times here..duplicates may occur as some bigrams e.g. both start with ‘T’, e.g. TE, TI, TO etc..).

QT

Added a third and fourth string. Might be not the best configuration, however at least there is an example of how the method might – sooner, later or never – works. Below you can find four words complying with Z homophones. The four words that were found digitally are ‘SOFTNESS’, ‘STUDIO’, ‘ENOUGH’, ‘COASTS’. An additional word can be completed (‘STATION’). Except the last one, all words have been found by the Python FCCP-model:

Not the correct solution yet.

QT

Small update..at one position of the cipher, the + symbol occurs twice with only one other symbol inbetween (line 9). Assuming the + symbol to represent either ‘S’ or ‘L’, the symbol inbetween (a ‘reversed’ B) can only represent a limited amount of letters, e.g.

S _ S

99% only the letters [‘A’, ‘E’, ‘G’, ‘H’, ‘I’, ‘K’, ‘M’, ‘O’, ‘P’, ‘S’, ‘T’, ‘U’] would occur. (e.g. ‘..TASKSOTHAT..’ but not ‘..SQS’…).

Only a small find, however it helps eliminating certain letters for the reversed B symbol in case the ´+ symbol represents ‘S’ or ‘L’.

QT

FCCP method slooowly delivers some results…now have five different strings with words found in it (some of them too short, imo..and not easy to make them longer). The following is just an example of how such a result may looks like. Five words found with no interference regarding the symbols (‘SOFTNESS’, ‘RENDER’, ‘SISTER’, ‘NEEDED’, ‘COASTS’).

QT

Hi, I welcome your points and would like to reply to them:

>>>This is all based upon the assumption that the 340 is a standard homophonic substitution cipher?
That is correct..it’s my focus. The 340 – as a homophonic substitution is extremely hard to crack…mostly because of shorter text length, an additional amount of homophones, lack of sequences etc. The 408 was homophonic substitution, too, which is why I focus on such regular homophonic substitution.

>>>Isn’t there enough evidence to point to some type of transposition step also being involved in the encryption?
To be honest, I see almost none. I know there is a discussion about transposition but at the same time I actually see no requirement for that. The cipher is difficult enough to crack even without any transposition of all those homophones. Other encryption methods actually do have transposition as a component of the encryption itself, the homophonic substitution usually has not (nor had the 408). It would represent some sort of two-step encryption (imagine an extremely difficult cipher, then encrypting it again..why?).

>>>If this was just a standard homophonic substitution cipher it would have already been solved.
Definitely not…we talk about 63^26 possible combinations of how letters can be placed on the homophones used. Additionally, the cipher lacks of 4- and 5-grams. Only two repeating trigrams, that’s it. Beyond that, Z had shuffled the sequences when using the homophones. iMO this makes e.g. ZDK which is a great tool almost unable to solve it (because it is based on the sequences). You can use Tianhe-2 for 2,000 years to play all the 26^63 variations..

>>>..it seems like making a collection of all different types of ciphers, would be more beneficial..
95% of ciphers use alphabetical letters or numbers in its code. Others use symbols, usually for substitution of letters (e.g. freemason). The 340 has more than 26 (or 20) homophones, thus it is (99% sure) a regular homophonic substitution. I don’t know any other polyalphabetic substitution with symbols. So far, we don’t know if any transposition has been used . I see no requirement for that (26^63..). Even think that Z had underestimated the effect of doing both, using more homophones as well as shuffling the sequences. He probably was not amused when his first cipher was cracked by a teacher.

>>>Jarlve got a solve on one of my ciphers while it was still transposed!
If Jarlve had considered the transposition, too, it then makes the cipher a regular homophonic substition again.

IMO there is only one single issue pointing towards a transposition and this is the circumstance that the homophone sequences are shuffled in the 340. E.g. the ‘w’ symbol shows up quite frequently in some areas of the cipher, in others not at all. Same is with many other homophones. If Z didn’t shuffle the sequences, a transposition may be considered (if you do believe in such a two-step encryption). Personally I see the strength of the 340 (not only because it hasn’t been cracked but because of the higher amount of homophones). This makes me step-off a bit from the idea of an additional transposition but I definitely can’t rule it out.

QT

A second partial result found:

Words found were RELEASE, SISTER, REPEAT, RETIRE, PARTIES

There might me more ‘results’ (or none)..those were just first examples. It obviously is not the 100% correct one. Will continue to search for one which is solvable as a whole, keep you updated.

QT

>>>This is all based upon the assumption that the 340 is a standard homophonic substitution cipher?
That is correct..it’s my focus. The 340 – as a homophonic substitution is extremely hard to crack…mostly because of shorter text length, an additional amount of homophones, lack of sequences etc. The 408 was homophonic substitution, too, which is why I focus on such regular homophonic substitution.

The extra difficulty over the 408 from the shorter text length and additional amount of homophones is trivial and lack of sequences do not matter one bit. As far as I know, ZDK does not use sequences nor does AZdecrypt. And such hill climbers trample 26^63 with ease and more-or-less proof that there is no high scoring plaintext solution available for the 340. You will run into the same problem with your FCCP method.

It is impossible to come up with a coherent full cipher horizontal plaintext solution of reasonable quality for the Zodiac 340 cipher.

Hi Quicktrader,

I think it is very important to try as many approaches to z340 as possible. I believe it is almost certain that transposition was used, but hey…there is no definite proove yet since a solution has not yet been found.
Nevertheless, I agree with Jarlve: if z340 is a z408-like cipher, it would have been solved long ago. No matter if 63 or 80 symbols, no matter if cyclical or not.
But that’ s just my opinion. What would be interesting, however, would be a z408-like cipher with 340 characters without transposition, which cannot be solved by an automatic solver. I can only imagine such things if the plain text is extremely absurd or contains numbers (e.g. a list of dates, names and locations).
Are there sample ciphers of normal homophonic substitutions with the properties of z340 that cannot be solved by automatic solvers?

Translated with www.DeepL.com/Translator

@Jarlve

Regarding ZDK
Have a look in the ‘contact analysis’ section..it might or it might not be based on sequences, anyway. I absolutely appreciate this tool.

Regarding extra difficulty:
408-cipher: 26^63 = 139098011710742195590974259094795403842655842142490330518716727403333474672708595090456576
340-cipher: 26^54 = 25618918401207524005916276251028099629855783828009607898193480161907468926976
Sure about that? Each digit more (or less) is 10 times more variations..a difference of 13 digits means a x1000,000,000,000 higher amount of combinations that have to be ‘cracked’..

Regarding "You will run into the same problem with your FCCP method.":
We will see…it definitely could happen easily.

Regarding "It is impossible to come up with a coherent full cipher horizontal plaintext solution of reasonable quality for the Zodiac 340 cipher."
You know this is not correct..it is more likely that the cipher is a normal ‘homophonic substitution’ than a ‘homophonic transposition-substitution’. But it’s ok to believe in the opposite (like Largo said, sort of, multiple approaches increase the chances of the cipher to get solved). I even do believe that there are multiple solutions for the 340, if you only choose your words ‘wisely’ (and short ones). With words such as I, AS, DID, DO, GO, FAT, CAT etc. you are almost capable to fill out the cipher (but then without any logical sense of the cleartext).

@Largo:
To give an example why not all homophonic substitutions can be solved: Take a 340 cipher with 340 different homophones. You won’t solve it. Nor will any supercomputer. You may be able to write any text into the cipher, but you surely won’t figure out the original cleartext. Or, alternatively imagine a homophone substition with no bigrams, trigrams or other n-grams. It wouldn’t be easy to solve that one either.

QT

To give an example why not all homophonic substitutions can be solved: Take a 340 cipher with 340 different homophones. You won’t solve it. Nor will any supercomputer. You may be able to write any text into the cipher, but you surely won’t figure out the original cleartext.

Of course, you are right. In this case we are talking about an one time pad. This is not solvable. But z340 does not seem to be an OTP. Even if it is, why are you trying to solve it when it’s impossible?

408-cipher: 26^54 = 25618918401207524005916276251028099629855783828009607898193480161907468926976
340-cipher: 26^63 = 139098011710742195590974259094795403842655842142490330518716727403333474672708595090456576
Sure about that? Each digit more (or less) is 10 times more variations..a difference of 13 digits means a x1000,000,000,000 higher amount of combinations that have to be ‘cracked’..

Jarlve-test-cipher: 26^100 = 3142930641582938830174357788501626427282669988762475256374173175398995908420104023465432599069702289330964075081611719197835869803511992549376 (142 decimal digits)

Not a problem to crack at all. The search space is not the issue here but the multiplicity is. Consider the Beale 2 cipher which has 182 symbols. Or some of my personal test ciphers with over 500 symbols. Say 26^500. Now that is 708 decimal digits and these still solve because the ciphers are also longer. It is about the ratio of symbols to the cipher length (multiplicity) and that is why 26^54, 26^63 or 26^100 does not mean anything. The 340 has a multiplicity of 0.185 (63/340) and that is not very difficult.

1   2   49  3   4   35  56  39  70  86  64  80  7   25  8   7   75
33  9   47  10  11  12  13  59  96  68  50  13  65  46  15  12  28
16  17  79  66  60  74  87  61  24  8   18  94  41  12  71  84  76
26  90  3   54  57  70  78  5   6   19  62  52  20  93  27  51  58
1   48  95  97  92  42  83  69  85  55  98  100 31  4   10  11  79
72  25  43  26  64  49  13  53  82  33  15  46  65  14  36  27  66
80  47  89  8   12  65  37  71  56  24  40  67  83  44  45  2   39
68  77  35  86  75  57  61  73  29  59  74  91  96  90  6   80  96
21  99  98  29  94  84  16  58  51  46  72  95  81  76  69  50  52
67  56  5   6   99  22  7   94  85  99  48  28  94  60  100 87  13
58  34  92  64  38  92  53  14  55  69  53  97  11  66  93  4   14
68  54  71  80  23  8   79  85  89  83  10  3   65  77  17  41  88
78  74  82  37  6   62  69  2   84  76  25  9   33  61  84  7   40
85  95  73  44  1   81  1   98  100 97  45  53  19  82  47  90  78
36  60  59  87  88  54  52  67  31  4   89  25  38  46  32  5   78
48  7   37  18  26  20  62  28  33  27  64  36  37  2   39  14  91
25  49  16  40  63  33  35  56  70  70  47  20  88  86  75  57  9
59  10  8   43  47  15  30  98  52  45  21  59  72  96  19  50  67
39  66  83  68  93  60  34  99  23  77  12  24  30  64  11  29  94
31  58  28  26  79  13  92  23  73  12  88  87  70  75  81  18  30

Well, two thoughts..Beale forget, it’s a book cipher. Not comparable at all. Second, the cipher length, of course, matters. The ratio between what you call search space to the cipher length is critical.

If we look at the multiplicity

54/408 = 0.132 or an average of 7.55 letters per homophone

and

63/340 = 0.185 or an average of 5.40 letters per homophone

Thus, regardless of the cipher length, the 340 has a 40% different multiplicity than the 408. This, however, is only the RATIO between the homophones used and the length of the cipher. It doesn’t say anything about the complexity of the cipher, which may increase overproportionally to its multiplicity and may also depend on e.g. words used, accidential distribution of n-grams etc..

When running ZDK, I indeed got a solution on the first try (numeric). When I shuffled the key (F5), however, I didn’t get the result anymore. Are you able to always solve the test cipher? Indeed it delivers a great result.

Have the homophones in your test cipher been used in sequences?

QT