My Math Forum Help needed !... Cryptology.. symbol to letter odds formula.

 September 3rd, 2011, 02:40 AM #1 Member   Joined: Aug 2011 Posts: 89 Thanks: 0 Help needed !... Cryptology.. symbol to letter odds formula. Hello again. I'm a Swedish historian and not a mathematician. This question might be trivial... 1. If a person finds a set of symbols, that is not part of any known historic or modern written language. 2. The person can with the help of simple symbol to letter exchange get an understandable sentance in a known language. Is it possible to calculate the odds that this understandable sentance is the result of pure coincidence, and not part of any original design man-made by the person who wrote the symbols ? Is it possible to construct a formula for this ? Thank you. Would appreciate help on this.
 September 3rd, 2011, 06:36 AM #2 Senior Member   Joined: Jun 2011 Posts: 298 Thanks: 0 Re: Help needed !... Cryptology.. symbol to letter odds form I am neither a mathematician nor a historian, but I am entitled to have a point of view? From what I read, a secrete can be encrypted and the chance of it being discover can be computed, but as far as deciphering the meaning a symbol can only be computed from a collection of data about the symbol in every uses. For example, the probability of occurrence letter b in forming up a meaningful German can be computed from how the letter is used in German language. As for an unknown symbols, what reference is there to be used? I read the story about how the German code was broken in WWII. Well, it was impossible to break until several code books were stolen from sunken German submarines, and only having that as a reference, the US Navy ran many computers 24/7 to hasten the change of hitting a meaningful message from the German military. Some loony said Shakespeare's books have hidden messages, but no secrete was ever discovered because there wasn't a secrete. The probability of finding the meaning of an encrypted message with no reference is null. It's either discovered or not discovered. Ah, I think, I will make a lot of math people mad.
 September 3rd, 2011, 08:16 AM #3 Member   Joined: Aug 2011 Posts: 89 Thanks: 0 Re: Help needed !... Cryptology.. symbol to letter odds form I interpreted the last post as an oppinion regarding ciphers. What I need is help constructing a formula... - Lets say you have sequence of symbols that concists of 15 DIFFERENT symbols, in series concisting of 45 symbols total. - It is possible to exchange the 15 different symbols to letters in the alphabet of a language, and the sequence form an understandable sentence in that language. What I need is a formula that calculates the odds that this can be the product of pure coincidence. In other words... a % that the sentence can be derived from the symbols without it beeing intended by the writer of the symbols. Is this possible ?
September 3rd, 2011, 11:44 AM   #4
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Re: Help needed !... Cryptology.. symbol to letter odds form

Quote:
 Originally Posted by TheSwede I interpreted the last post as an oppinion regarding ciphers.
Yes, it helps to break boredom. It will bring in some mathematicians to open their mouths for you.
Quote:
 Originally Posted by TheSwede What I need is help constructing a formula... - Lets say you have sequence of symbols that concists of 15 DIFFERENT symbols, in series concisting of 45 symbols total. - It is possible to exchange the 15 different symbols to letters in the alphabet of a language, and the sequence form an understandable sentence in that language.
Give an example so that they have an idea about what you mean. A picture is worth a thousand words. You will be surprised. Sometimes it doesn't take a mathematician to give an answer you want.

Quote:
 Originally Posted by TheSwede What I need is a formula that calculates the odds that this can be the product of pure coincidence. In other words... a % that the sentence can be derived from the symbols without it beeing intended by the writer of the symbols. Is this possible ?
Have you tried permutation and combination? I hope you are not annoyed. Just in case you don't known, I am also very interested in knowing the mysterious thing you are working on. I was told that historians are very smart people. If I am not smart enough to understand what you want, then I will sit back and watch the heavy weight mathematicians showing the good stuff.

 September 4th, 2011, 12:42 AM #5 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: Help needed !... Cryptology.. symbol to letter odds form I'm not a mathematician nor a historian either. So just throwing in a mostly uneducated opinion. You could certainly figure out the possible permutations of how you could substitute letters for the symbols. (I'd have to think about how and I'm too tired to even decide if that's as simple as it sounds like in my head. Statistics, tired and wine really don't play nice together :P ) But it seems to me you could never figure out the odds that you could, by coincidence, accidentally form a proper sentence. You might see 15 symbols, but how do you know the number of symbols that exist that were not used? OK, let's assume you have a way to know there's only 15. There's still the fact that it's unknown how these symbols work, if and in what cases the order of them matters - not only in terms of making a sentence, but are the symbols words, or are some words and some need to have two or three symbols to make words (or ideas), or are all of them letters and they form words the way (most of) our current languages do? You wouldn't know anything about how the symbols work together to form sentences to know what the possibilities are. If you don't know what the possibilities might be (including things we perhaps have never thought of), how could you figure out the odds? Maybe I'm totally screwed in the head, but that's my opinion. On the other hand, I think the chances of that happening completely accidentally are so improbably teensy weensy that statistically it probably doesn't even matter. As a historian, you've got some kind of knowledge to give you something to go on to at least start making education guesses, right? Or at least you hire a linguist. That's not by accident.
September 4th, 2011, 02:18 AM   #6
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Re: Help needed !... Cryptology.. symbol to letter odds form

Quote:
 Originally Posted by Math Dreamer I read the story about how the German code was broken in WWII. Well, it was impossible to break until several code books were stolen from sunken German submarines, and only having that as a reference, the US Navy ran many computers 24/7 to hasten the change of hitting a meaningful message from the German military..
I think you will find that it was the British (with help from Poland) that broke the Enigma code, and it was only the required brute force computations that the US helped with :P

September 4th, 2011, 05:52 AM   #7
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Re: Help needed !... Cryptology.. symbol to letter odds form

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Originally Posted by mattpi
Quote:
 Originally Posted by Math Dreamer I read the story about how the German code was broken in WWII. Well, it was impossible to break until several code books were stolen from sunken German submarines, and only having that as a reference, the US Navy ran many computers 24/7 to hasten the change of hitting a meaningful message from the German military..
I think you will find that it was the British (with help from Poland) that broke the Enigma code, and it was only the required brute force computations that the US helped with :P
What you said is true for the codes before Enigma. I have read the book The breaking of the Enigma 6 different times, while the first read was when I was in grade 3. I was so wrapped up in wanting to be in that kind of work, a childhood dream, that I read and read and read the book although I did not know every mathematical term, but I truly learned that there was no breaking of Enigma until the first code book was discovered from a sunken submarine. Only then the MI6 and CIA began to figure how the rhythm of the Enigma machine work. Without know the rhythm, not even a computer could do it. You may say by brute force, but brute force is a complementary necessity of all mathematical knowledge because human life is finite, and shorter then human life is the life of a secrete code. Think of it, every time after sending a message, the machine automatically scramble the original code so that the last code become obsolete, and by the time it's obsolete, calamity had befall the free world. You have to give credit for the sophistication of the German Nazi despite they lost the war. Hey, we won by brute force too. Just think how many people died to win the war; it's too many against a small number of sophisticated Germans.

I owe Mr Swede apology for derailing from answering his questions, so I will make up for him in the next post.

September 4th, 2011, 06:20 AM   #8
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Re: Help needed !... Cryptology.. symbol to letter odds form

Quote:
 Originally Posted by TheSwede - Lets say you have sequence of symbols that concists of 15 DIFFERENT symbols, in series concisting of 45 symbols total.
Suppose all 15 symbols is all there is and not a single more ever existed, Then out of 15, you can arrange it in this many ways to arrange distinct symbols , i.e., no repetition:

$15!=15\times 14\times 13\times 12\times 11\times \dots \times 2\times 1=1307674368000$ arrangements. Let's call it $x$. This is only for non-repeating symbols. For repeating symbols, the possibility is far, far worse. Read http://en.wikipedia.org/wiki/Permutation

Next, lay this 15 symbols vertically, adjoining the next 15 symbols till you get 45 columns of 15 symbols, and suppose that there is no repeated arrangement in all 45 columns, then you will have a combination of

$\binom{x}{45}$. Read http://en.wikipedia.org/wiki/Combination

Quote:
 Originally Posted by TheSwede - It is possible to exchange the 15 different symbols to letters in the alphabet of a language, and the sequence form an understandable sentence in that language.
It's possible by augmenting the arrangements by the same process, but the number is huge.

For each column of 15 distinct symbols assigned to a Roman alphabet will have

26!=4.032914611266057e+26 . This is a 26 digits number.

For a series of 45 distinct arrangements, there will be
$1307674368000 \times 4.032914611266057e+26$ possibilities. It's a 39 to 40 digits number.

I am sorry sir, you would need a fine linguist and the most vicous computer hacker to help you with this humongous task.

 September 4th, 2011, 08:49 AM #9 Member   Joined: Aug 2011 Posts: 89 Thanks: 0 Re: Help needed !... Cryptology.. symbol to letter odds form Ok I think I understand, but what I need is a formula with variables into which I can put number of different symbols and number of symbols total, letters in the language of the decipherment etc. Why ? I need a guide in cryptology for pedagogical reasons, to be able to explain the odds that a decipherment can be done but that the message is not created by the original code maker, but by coincidence. I understand that the odds are low for the example with 15 different and 45 total, but if I get a formula then it would be possible to try different values and see what happens. I understand that you mean the following... we calculate the number of combinations the symbols can appear in, and 1 : (the number of combinations) is the odds that the symbols end up in just the actual sequence that can be deciphered to a readable message in a language. Is this correct ?
 September 4th, 2011, 09:48 AM #10 Senior Member   Joined: Jun 2011 Posts: 298 Thanks: 0 Re: Help needed !... Cryptology.. symbol to letter odds form My math education is still at the bottom. I have not learned combinatorial, considering I am still in highschool. Cryptology is way beyond; it a graduate course in mathematics, but I will deal with you question at my level. As far as I know, the probability of hitting a desired arrangement of combination, it came from common sense; that is, Probability of favorable outcome = $\frac{\text{number of desired combinations}}{\text{total possible number of combinations}}$ If you want no repeating symbols, given you have one particular desire arrangement, the the probability = $\frac{1}{k!}$ where $k$ is total number of distinct symbols. I truly wish I could simply give you a formula, but by so doing I will lead you astray. Would you please sir consider getting a very simple book at your library and take a look at it and see whether this book is suitable for your goal. Here I would like to recommended a very nice, simple book for you taste that will ultimately reach you goal, and here is the book: Probability by Seymour Lipschutz, see http://www.amazon.com/Schaums-Outline-P ... 676&sr=1-1. Every University in the world must have at least one in its library. Also, please consult your peer at the math department of your university. I fear that I would mislead you to a dead end for such important work of yours. Perhaps, you might want to send a private message to CRGreathouse. He is one hack of a mathematician. I would like to give you an example of what I learned in the area some similar to your work. Example. Find the number of (a) combinationss and (b) permutations of four letters each that can be made from the word $Tennesse$. My solution: Case 1: $\fbox{t}\fbox{e}\fbox{s}\fbox{n}$ Number of combinations= 4Cr4 = 1 (it means 4 choose 4) Number of permutations= 4P4 = 4!=24 (it means give 4 distinct symbols choose all 4 for an arrangement) Case 2: $\fbox{n}\fbox{n}\fbox{e}\fbox{s}$ Combiniations: Choose doublet n's first gives 3Cr1, choose 2 other distinct characters gives 3Cr2 Add them up Permutations: $\frac{4P4}{2!}\cdot 9= 108$ Case 3: $\fbox{e}\fbox{e}\fbox{s}\fbox{s}$ The process is the same a above $3Cr 2$ and $\frac{4P4}{2!2!}\cdot 3= 18$ Case 4: $\fbox{3}\fbox{3}\fbox{3}\fbox{t}$ (1Cr 1)(3Cr1) and $\frac{4P4}{3!}\cdot 3=12$ Case 5: $\fbox{e}\fbox{e}\fbox{e}\fbox{e}$ $1Cr1= 1$ and $\frac{4P4}{4!}=1$ So that's how it's done. It's a very slow process. If you use computer program written for it, you can do it a a fly. This is not in the book, but the concept is in the book I recommended.

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