My Math Forum Help !... Need probability formula for historic cipher

 August 1st, 2011, 12:17 PM #1 Member   Joined: Aug 2011 Posts: 89 Thanks: 0 Help !... Need probability formula for historic cipher I need to get hold of a formula for a historic cipher where you insert variables, calculate, and get a coincidence factor. So that it is "this-and-this" chance that the deciphered message was NOT intended by the original code designer, but made up of a chain of coincidences. The ciphermethod I need the formula for is called "symbol to letter" cipher and is simple. A set of symbols are deciphered to a message in lets say English by exchanging the symbols to letters. How do a person calculate the chance that the de-coded message fits the symbols by pure coincidence ? This chance will of course decrease in relation to the number of symbols, and the number of different kinds of symbols etc, but I think it is possible to create a mathematical formula with variables in it ? Can someone out there help me with this ? I know too little math to do it. :P :P
 August 1st, 2011, 12:58 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Help !... Need probability formula for historic cipher There are several (somewhat related) things that you might be referring to and I'm not sure which you want. It could be the coincidence index which is used to break the Vigenère cipher. You might instead be asking for some technique for distinguishing false positives and false negatives. Or it might be a simple probability calculation based on the number of symbols in the two alphabets.
 August 1st, 2011, 10:25 PM #3 Member   Joined: Aug 2011 Posts: 89 Thanks: 0 Re: Help !... Need probability formula for historic cipher The easiest way I think is to explain it with a scenario... 1) A decipherer finds 30 symbols in a row which consists of dots, squares, triangles and circles etc. 2) Some of the symbols reappear several times. 3) He uses trial and error and end up with a decipherment in English, using symbol to letter exchange. 4) Now he need to know how high the probability is that the deciphered message is NOT intended by the code-creator, but a product of coincidence. 5) With this probability factor he can discuss his decipherment with other people. Is there a formula for this ?

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