Cracking The Enigma (II)

Continuing from my second blog, the links to the previous blogs are given below:

https://theqriusrhino.wordpress.com/2018/07/09/the-making-of-the-enigma-machine/

https://theqriusrhino.wordpress.com/2018/07/12/cracking-the-enigmai/

Rejewski had a profound insight that although the plugboard and scrambler settings changed, the number of links in the chains is purely a consequence of the scrambler. For instance, let us take an example let’s pretend that the day key required the letters S and G to be swapped as part of the plugboard settings. If we change this element of the day key, by removing the cable that swaps S and G, and use it to swap, say, T and K instead, then the chains would change to the following:

previously:

after swap:

As seen the numbers 3,9,7,7 remain constant. So instead of having to worry about which of 10,000,000,000,000 day keys was correct he had to worry about about the 105,456 scrambler settings associated with the number of links in a particular chain.

His team began to check each of 105,456 settings and catalogued the chain lengths generated by each one. It took an entire year  but he was finally ready  to unravel messages.

Each day, he would look at the encrypted message keys, the first six letters of all the intercepted messages, and use the information to build his table of relationships. This would allow him to trace the chains, and establish the number of links in each chain. For example, analyzing the 1st and 4th letters might result in four chains with 3, 9, 7 and 7 links. Analyzing the 2nd and 5th letters might also result in four chains, with 2, 3, 9 and 12 links. Analyzing the 3rd and 6th letters might result in five chains with 5, 5, 5, 3 and 8 links. As yet, Rejewski still had no idea of the day key, but he knew that it resulted in 3 sets of chains with the followingnumber of chains and links in each one:

4 chains from the 1st and 4th letters, with   3, 9, 7 and 7 links.

4 chains from the 2nd and 5th letters, with   2, 3, 9 and 12 links.

5 chains from the 3rd and 6th letters, with 5, 5, 5, 3 and  8 links.

Rejewski could now go to his catalogue, which contained every scrambler setting indexed according to the sort of chains it would generate. Having found the catalogue entry that contained the right number of chains with the appropriate number of links in each one, he immediately knew the scrambler settings for that particular day key. Rejewski was working just like a detective who might find a fingerprint at the scene of a crime, and then use a database to match it to a suspect.

However he still had to establish the plugboard settings. Although there were billions of possibilities it now became a straightforward task. He removed all plugboard cables and typed an intercepted message with the known scrambler settings. This resulted in mainly gibberish words but often some phrases could be recognized. For example a phrase “alliveinbelrin” could be made out that letters R and L are to be swapped and message would be “arrive in Berlin”. By similiar analysis the plugboard arrangement could be  identified.

The Impact and The Bombes

Rejewski’s attack on Enigma is one of the great accomplishments of cryptoanalysis. German communication now became transparent to the Poles. Rejewski now mechanized the cataloguing system. Rejewski’s invention was an adaptation of the Enigma machine, able to rapidly check each setting until it spotted a match. Because of the six possible scrambler arrangements, it was necessary to have six of Rejewski’s machines working in parallel, each one representing one of the possible arrangements(123 132 231 213 312 321). Together, they formed a unit that was about a meter high, capable of finding the day key in roughly two hours. The units were called bombes, a name that might reflect the ticking noise they made while checking scrambler settings.

The Challenge Not Yet Over

Rejewski’s skills eventually reached their limit in December 1938, when German cryptographers increased Enigma’s security. Enigma operators were all given two new scramblers, so that the scrambler arrangement might involve any three of the five available scramblers. Previously there were only three scramblers (labelled 1, 2 and 3) to choose from, and only six ways to arrange them, but now that there were two extra scramblers. Rejewski’s first challenge was to work out the internal wirings of the two new scramblers. More worryingly, he also had to build ten times as many bombes, each representing a different scrambler arrangement. The sheer cost of building such a battery of bombes was fifteen times the Biuro’s entire annual equipment budget!

The following month the situation worsened when the number of plugboard cables increased from six to ten. Instead of twelve letters being swapped before entering the scramblers, there were now twenty swapped letters. The number of possible keys increased to 159,000,000,000,000,000,000!

The Polish Revelations

As Poland could not benifit now from Rejewski’s works due to economic constraints, they decided to disclose the secrets to the allies. German onslaught was in full peak and Poland had a fear of invasion anytime soon. On a meeting, the bombes were shown to the British and French who were astonished to find the  breakthrough that the Poles had achieved. French forces were mainly suprised as it was they who had given the basic informations to the Poles due to utter ignorance. This small nation had really done a huge deal. Two weeks later on September, Hitler invaded Poland and the Second World War began

In my next blog I’ll come up with a new mind that finally made the Enigma cipher worthless and led to the victory of the allies. It was also he who laid foundations for programmable machines to be known in the present as ‘Computers’.

 So stay tuned guys for my next blog!

Thank you,

Shoubhik Banerjee

IISER Bhopal