Question About What Is Minimum Needed For Probable Solution

[AK Wilks]

As part of my semi - retirement farewell tour, I will be making one last (?) post here in Zodiac Ciphers. Part of that post will be a project I will ask some of our best code people and computer based code researchers to work on. A Mission (Probably) Impossible, should they chose to accept it.

But first a question. Most of you may know that I have done the majority of my code work and research by pen and paper. Other than a few runs and experiments here and there, for the most part I have not really mastered devising or using computer solve programs. That is the principal reason for my coming post and invitation for others to participate.

But first a question, directed to Glurk, Doranchak, Up2something, Jarvle and other creators and users of computer code solving programs. I realize that most who have worked on the 340 feel it is very likely that all or at least parts of it require something beyond a mere one stage solution. But for this next question, let's assume that all or at least a majority of the code is a one stage code.

What do you think would likely be the minimum amount of solved code symbols you would need to have one of the good code solver programs then be able to solve all or at least a good part of the code?

In other words, say we found Zodiac's notebook and it tells us what the frequently used + symbol in the 340 stands for. Taking that and that alone, putting it into your solution programs, would you expect that it would then solve a major part of the 340? A few lines? A few words?

What if in that Z notebook we found not only the correct translation for +, but also for about three lines of the 340? About maybe 15 to 20 symbols? Plugging that in, would you expect your program to be able to solve the entire code, the majority, part of it or just a few more words?

[EndOfTheWorld]

I've never looked at the codes. Not my bag. But I find it amazing that people are still trying to crack the codes after forty years. (1) is it not possible they are unsolvable? (2) if solvable but very difficult, doesn't this point to the likelihood of a math PHD or the like as the Zodiac?

[doranchak]

Thing is, a code like Z340 would be very quickly solvable by one of the cipher solving programs, if the cipher met our assumptions:
- It is written in English
- in a normal reading direction (left to right, top to bottom)
- Using simple homophonic substitution similar to how Z408 is made

The programs are good at solving these kinds of codes without requiring any advance knowledge of the keys, even for plaintext that has a lot of mistakes and misspellings.

But, Z340 fails to solve under those assumptions, so therefore one or more of them are wrong. At the moment we are only really beginning to look at all the possible variations of encoding that Z could have employed.

Z could tell us "+" means "E" but it won't really help unless he also says, "here's the encipherment method I used".

A worst-case-scenario version of that view would be: We could know the entire substitution key, and still be unable to solve the cipher, because the plaintext would have to go through another stage before being readable!

[doranchak]

Here is a simple example of that worst case scenario:

Let's say Z had decided to encrypt Z408's plaintext using columnar transposition using the key "ZODIAC". That would turn this plaintext:

ILIKEKILLINGPEOPL
EBECAUSEITISSOMUC
HFUNITISMOREFUNTH
ANKILLINGWILDGAME
INTHEFORRESTBECAU
SEMANISTHEMOATDAN
GERTUEANAMALOFALL
TOKILLSOMETHINGGI
VESMETHEMOATTHRIL
LINGEXPERENCEITIS
EVENBETTERTHANGET
TINGYOURROCKSOFFW
ITHAGIRLTHEBESTPA
RTOFITIATHAEWHENI
DIEIWILLBEREBORNI
NPARADICESNDALLTH
EIHAVEKILLEDWILLB
ECOMEMYSLAVESIWIL
LNOTGIVEYOUMYNAME
BECAUSEYOUWILLTRY
TOSLOIDOWNORSTOPM
YCOLLECTINGOFSLAV
ESFORMYAFTERLIFEE
BEORIETEMETHHPITI

into this:

ENLUSHIFNNGTRCAEA
UALLHVHTIEIEEGGOF
GEATEDLBPCLHLLMAI
GUESITDSCTSFFFRET
KGESSFSUKGAHEANMN
ELTSIEEHNRTNREYCW
IBRIWILOAELALLEVL
IMBELOOTOILOTEITI
ILOCTUIRHLLIOBETT
RAAIEGEALXCETAIRO
HTTFHNWRIDDEKWCSI
OYAAUROOMEOEYLEEP
KIPAICTEAIDNREMHD
TMLLTITTLPEVTNNRF
AHPIAIIENIAIIIOLW
TOMUWYIRYCFSAIOMI
LLEEIMNOTLIEFTSSA
ENFKMGMOIENSEHTUS
TLSOTEIENANHEDEYS
NENCOTLNPLGVMRBTH
IIPBEOUMNIWMESUIO
GAOOONSMRGEIBTTOK
IRETAHEBRRSTVEBME
LVYEYLSWOLNAREEEH

Then, he encodes that new plaintext using simple homophonic substitution.

Now, we come across his secret notebook which allows us to recover that second plaintext. We still need to figure out that there is a columnar transposition step, and the keyword is "ZODIAC".

Something like that might be happening with Z340!

[AK Wilks]

EOTW - Many have debated the solvability of the code. Some think it is just nonsense. But the FBI (and others) have stated that the structure seems to indicate it likely is a real code.

There are things like a one time pad and other methods whereby a person of normal intelligence could create a code that would be extremely difficult to solve to virtually unbreakable. But I think his dedication to the code, it's construction and so far unsolvability indicate that Z was likely someone of high intelligence, probably with interest in and knowledge of codes and/or math.

Doranchak - I see the problem. For reasons I'll explain later, I do think that part of the 340, maybe a third or so, is a normal one stage homophonic substitution cipher. If that is true, if you had the correct translation of + and maybe 12 to 20 other symbols, do you think your program would be able to solve this part of it?

[doranchak]

Maybe. Depends on the length of the chunk of cipher text, and how many different symbols are in it.

If it has too many different symbols, then it will be much harder to find the plaintext (assuming a normal plaintext exists for it).

The chance of recovering plaintext for a normal homophonic substitution cipher goes down when the length gets shorter and/or the number of distinct symbols increases.

[Quicktrader]

LDefinition.xlsx

Open 'Bernoulli_Stat2'..

This is the answer to your question regarding the + symbol. According to Bernoulli, only the L or the S are viable solutions for the + symbol (as a double letter). S should be preferred as it is closer to the overall amount of + symbols than L.

QT

[Jarlve]

LDefinition.xlsx

Open 'Bernoulli_Stat2'..

This is the answer to your question regarding the + symbol. According to Bernoulli, only the L or the S are viable solutions for the + symbol (as a double letter). S should be preferred as it is closer to the overall amount of + symbols than L.

QT

For what it is worth, AZdecrypt solves it as being a "T". And is consistent for different n-gram sizes and normalizations.

[Jarlve]

Doranchak - I see the problem. For reasons I'll explain later, I do think that part of the 340, maybe a third or so, is a normal one stage homophonic substitution cipher. If that is true, if you had the correct translation of + and maybe 12 to 20 other symbols, do you think your program would be able to solve this part of it?

My solver, AZdecrypt has solved up to a multiplicity of 0.5 although that is probably an extreme case. Simply divide the number of unique symbols by the total number of symbols. For the normal 340 this is 63/340=0.185294 multiplicity.

If your cipher is not higher than 0.5 (and preferably not higher than 0.4) than I'm willing to give it a try for you. Though the answer at these difficulty levels will not be definitive and it may a few days of computer time.

[AK Wilks]

QT - Is that based on a study of general use (newspapers, books, erc.), or a specific analysis of Zodiac letters and the solved code? Because as your study showed, backed up by examples from Glurk, Doranchak and myself, Zodiac used far more LL and L words than the average person. KILL, KILLING, THRILL, WILL, SHALL, SLAVES, POLICE,etc. This will all be part of my more detailed up coming post.

Jarvle - Thanks for being willing to take this on, hopefully others will follow after they read my upcoming post. I am talking about the 340. I will provide the suggested translation of the + symbol, and about 2 1/2 lines. So maybe 15 to 20 other symbols?

I'll try to make the post tonight or more likely tomorrow.