Play with it ๐Ÿ˜Ž

Write a message, we will encrypt it with symbols (here emoji ๐Ÿ˜‰) by replacing each alphabet letter with symbols. Then our algorithm will try to reconstruct the original message.

What’s the problem ๐Ÿ™‹

Between 1968 and 1970, a serial killer nicknamed the Zodiac Killer murdered at least 5 people in the San Francisco area, and he is probably responsible for several dozen other unconfirmed cases. He was known for taunting the authorities by sending letters to local newspapers that contained such coded messages. The killer was never identified, and the case has been officially open for over 50 years.

The encryption of the message was done by changing the characters of the alphabet by symbols in order to make the message incomprehensible. So our goal is to find these correspondences to the rigth character in order to reconstruct the real message. In the next section we will see that we can solve this problem using optimization.

I first get in touch we this problem while I was watching a French science channel video on the topic (ScienceEtonnante). I just try to reproduce and make it online so people can challenge the algorithm.

Solve it as combinatorial optimization problem ๐Ÿงฎ

In reality we are dealing with a combinatorial optimization problem. The objective is to assign the symbols to the letters of the alphabet to reconstitute the message. For that we will need a score that will allow us to evaluate our solution. Here our score function will be the plausibility that the reconstrcution we obtain is plausible in the language we are considering (Here English).

Plausibility as objective function

Our objective function will use the bi-gram probabilities. The matrix below represents the character chaining probabilities that we obtain by parsing the book.

The solution

Once we have our function, all we have to do is apply a stochastic optimization algorithm and we are done. Here we will apply the simulated annealing algorithm.