World Mysteries - Zodiac Killer Letters - Greatest Unsolved Mysteries

World Mysteries - Zodiac Killer Letters - Greatest Unsolved Mysteries

During the 1960s and 1970s, there was a certain criminal in the San Francisco Bay area that was identified as the Zodiac killer for the mind-boggling letters he sent to the police and to the press. Although one of the four letters were cracked, which contained a very disturbing message, the other three have never been identified, even until now.

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World Mysteries - Zodiac Killer Letters - Greatest Unsolved Mysteries

Zodiac Killer code cracked?

In the late 1960s early 1970s a serial killer code named Zodiac sent encrypted letters to the local newspapers taking credit for the killings and warning of more to come. The first letter's code was cracked in 1969 by an amateur and now the most famous of the set, a 340-character letter, has been cracked by another amateur.
The main proof that the message has been cracked is simply that the result is meaningful:

KILL/SLF/DR/HELP/ME/KILL/MYSELF/GAS/ 
CHAMBER/AEIOUR/DAYS/QUESTIONSABLE/ 
EVERYY/WAKING/MOMENT/IM/ALIVE/MY/ 
PRIDE/LOST/I/CANT/GO/ON/LIVING/IN/THIS/ 
WAY/KILLING/PEOPLE/I/HAV/KILLD/SO/MANY/
PEOPLE/CANT/HELP/MYSELF/IM/SO/ANGRY/I/
COULD/DO/MY/THING/IM/ALONE/IN/THIS/
WORLD/MY/WHOLE/LIFE/FUL/O/LIES/IM/
UNABLE/TO/STOP/BY/THE/TIME/YOU/SOLVE/
THIS/I/WILL/HAV/KILLD/ELEVEN/PEOPLE/
PLEASE/HELP/ME/STOP/KILLING/PEOPLE/
PLEASE/MY/NAME/IS/LEIGH/ALLEN/

One of the main suspects was called Leigh Allen so it really does all fit.
The proof of decoding is that you have something intelligible and this is a long-standing principle of cryptography.
So end of story, the code has been cracked.
Well no not really.

The principle used to detect a successful decode depends on the use of a regular algorithm to decode the message. The algorithm can be complex but it has to have a regularity that is controlled by a small number of parameters. If you allow too many degrees of freedom in the decoding algorithm then it can be "arranged" to produce a result that is meaningful but has no connection with the original plain text. 

If you look more closely at the decryption process used on the Zodiac letter it begins to reveal rather too many degrees of freedom. First the non-alphabetic symbols are converted to the alphabetic characters they most resemble. This part is reasonable. Next it is assumed that the code is a modified Caesar cipher, i.e. where each character is mapped to another in the alphabet with a constant shift. For example a Caesar cipher with a shift of 3 maps A into D.

As most programmers know, the Caesar cipher is easy to crack because it preserves the usual n-gram frequencies of character used in a language. If the Zodiac letter were a simple Caesar cypher it would have been decrypted long ago and this argument has been used to suggest that the current cracking of the code by an amateur must be a hoax.
However this reasoning is wrong because the code used in the cracking isn't a simple Caesar cipher but a form of Vigenère cipher. In this case the shift is varied in a regular pattern as specified by a key. For example if the key is 1234 you would shift the first letter by 1, second by 2 and so on. When the key is used up you start at the beginning again.This too is easy to crack if the message is long enough because the key is used repeatedly and this introduces statistical regularities which can be used to find the key. However if you use a key as long as the message and only use the key once - a so called one time pad - then the code is uncrackable. So it all depends on how many degrees of freedom the key is given.

How The Zodiac enciphered the Zodiac 408 cipher

World Mysteries - Zodiac Killer Letters - Greatest Unsolved Mysteries

I was looking through the Zodiac Killer ciphers the other day and woke in the middle of the night wondering how The Zodiac actually enciphered the first message (the one that was decoded).

The message consists of 408 symbols; there are 54 different symbols used for the alphabet. So there are multiple symbols for each letter of the alphabet. The Zodiac used a homophonic cipher to disguise the most common letters of the alphabet by using multiple symbols for common letters. For example, for the letter E The Zodiac used seven different symbols.

I started to wonder how when The Zodiac was writing out the message he picked which symbol to use. And it occurred to me that he might have used a really simple system: cycling through the symbols for each letter in the same order.

A quick look at the cipher showed that it was likely that the simple scheme was used. Here I looked at the letter E and the letter N and discovered that a simple pattern was used for each.

An attack would consist of the following:

1. Split the Zodiac 340 cipher on each of the symbols to obtain a list of lists of sequences

2. Remove any duplicated characters from the lists (since we can assume that there will be none if the characters are being used in order as in the Zodiac 408)

3. Generate all combinations of the first list and look for the same subsequence occurring in the other lists.

Looking at the Zodiac 340 it looks like it splits on average into deduplicated strings of between 20 and 30 symbols. If we look for subsequences of length say 6 then each search would require 38,760 and 593,775 combinations to be generated. For 63 characters that sets an upper bound of roughly 37m combinations. That leads me to think that this approach could be used.

World Mysteries - Zodiac Killer Letters - Greatest Unsolved Mysteries