1932: mathematicians Rejewski, Zygalski, and Różycki began work at the Polish Cipher Bureau. Rejewski was tasked to work on Enigma decryption. With math formulas and stolen Enigma instructions, Rejewski determined Enigma machine structures; Poland began building Enigma replicas. ​​​​​​​

“The poles had a brilliant mathematician who broke it on permutation theory.” - Batey

     1935: Rejewski devised a system: "catalog-card." By hand, they compiled catalogs of Enigma permutation cycles. Comparing code patterns with his catalog, Rejewski determined the code’s daily ground-settings. His catalog listed the characteristic cycles of the 6-X-17,576 basic positions. He invented a mechanical “cyclometer” to help. ​​​​​​​

     Unfortunately, their technique became useless; September 1938 saw Enigma complications. The Poles initially cracked ciphers manually, but because the Enigma became too complex, they would utilize machinery. Similar to the “catalog-card,” Zyglaski created perforated sheets for finding Enigma settings. Codebreakers began cataloging different patterns called "females,” which were letter repeats revealing rotor positionings. 

"This time, however, the catalog would indicate which of the 105,456 combinations of initial rotor settings (17,576) and wheel orders (6) could give rise to such repeated cipher letters three positions apart. Henryk Zygalski quickly worked out a system for encoding the information onto sheets."

"For each repeat discovered in a day's batch of Enigma signals, the sheet corresponding to the initial left rotor setting of that message would be placed on a light table. Each sheet would be aligned so that the square corresponding to the initial position of the middle and right rotor was at the upper left-hand corner of the light table ... Scanning left to right or up or down over the stacked sheets would then be the equivalent of shifting the middle and right ring settings of all messages simultaneously. Anywhere light shone through corresponded to a ring setting that would permit the repeats to have occurred at all of those relative initial rotor settings."

     Using these, they discerned whether cipher-texts had "females.” Due to vast cataloging amounts, Rejewski created the “bomba” for searching. Taking over what now was too great for humans, this machine roughly ran through Enigma settings.

     1939: Unfortunately, Germany incorporated 6 more sockets to the plugboard, vastly decreasing the bomba's effectiveness. It was never readjusted before invasion; Germany invaded Poland, prompting Poland to desperately share everything about the Enigma with France and Britain. They revealed their efforts and shared bomba plans.

"In July 1939 Denniston and Knox were invited to Warsaw by the Poles to discuss "E." It then was disclosed that the Poles had been successfully dealing with a large amount of "E." Denniston's impression is that the Poles' continuity ran well back into the early twenties. They had bombes. Knox was outraged that the Poles had been reticent in February; not realizing that the Poles understood English, he made very derogatory remarks while riding in a cab with Denniston and one of the Poles, to Denniston's great embarrassment ... Before GC+CS got well into "E" traffic, war broke out."

     Poland disclosing code secrets initiated Britain to recruit more mathematicians at Bletchley Park, the cryptography center. Enter Alan Turing.