The Theorem that Won the War: Part 3 – Breaking Enigma

While the Allies couldn't acquire the daily keys we looked at in Part 2.4, they could acquire “sigint” (signals intelligence):  the message keys were transmitted by radio, and the Allies could eavesdrop. At first glance, this doesn't seem useful, since the message keys would be encrypted. But there's one more factor: to ensure the message key was received, the Germans sent it twice. This meant that the Allies could determine two different encryptions for the same letter. We now explore how this allowed the Allies to take advantage of the theorem that broke Enigma and won the war.

We will again proceed in several parts, pausing to look at some specific activities along the way.

• Part 3.1: Cycle Decompositions
  • Activities for Part 3.1
• Part 3.2: Rejewski’s Theorems
  • Activities for Part 3.2
• Part 3.3: Breaking the Full Enigma
  • Activities for Part 3.3

Figure 19. Bletchley Park mansion, headquarters of the Enigma code breaking effort.
Photograph by Matt Crypto, public domain.