Kasiski enlisted in East Prussia’s 33rd Infantry Regiment on 20 March, 1823 at the age of 17. In May 1824, he was promoted to the rank of Master Sergeant, and eight months later was commissioned as a Second Lieutenant in February 1825. It took fourteen years to earn his next promotion when, in May 1839, he advanced to the rank of First Lieutenant. His next advancement was quicker, promoted to Captain in November 1842. Kasiski finally retired from active service with the rank of Major on 17 February 1852.

Between 1860 and 1868 he was the commander of a National Guard battalion.

In 1863, Kasiski published a 95-page book on cryptography, Die Geheimschriften und die Dechiffrierkunst (German, “Secret writing and the Art of Deciphering”). This was the first published account of a procedure for attacking polyalphabetic substitution ciphers, especially the Vigenère cipher (although it is possible Charles Babbage was already aware of a similar method but had kept it secret). The method relied on the analysis of gaps between repeated fragments in the ciphertext; such analysis can give hints as to the length of the key used. This technique is known as Kasiski examination.

The significance of Kasiski’s cryptanalytic work was not widely realised at the time, and he turned his mind to archaeology instead. The later years of his life were spent at Neustettin (Szczecinek); the 11th edition of Encyclopædia Britannica cited a scholarly article by Kasiski in its entry on the town. Historian David Kahn notes, “Kasiski died on May 22, 1881, almost certainly without realizing that he had wrought a revolution in cryptology” (The Codebreakers)

While studying mathematics at Poznań University, Rejewski had attended a secret cryptology course conducted by the Polish General Staff’s Cipher Bureau, which he joined full-time in 1932. The Bureau had achieved little success reading Enigma and in late 1932 set Rejewski to work on the problem. After only a few weeks, he deduced the secret internal wiring of the Enigma. Rejewski and his two mathematician colleagues then developed an assortment of techniques for the regular decryption of Enigma messages. Rejewski’s contributions included devising the cryptologic “card catalog,” derived using his “cyclometer,” and the “cryptologic bomb.”

Five weeks before the German invasion of Poland in 1939, Rejewski and his colleagues presented their results on Enigma decryption to French and British intelligence representatives. Shortly after the outbreak of war, the Polish cryptologists were evacuated to France, where they continued their work in collaboration with the British and French. They were again compelled to evacuate after the fall of France in June 1940, but within months returned to work undercover in Vichy France. After the country was fully occupied by Germany in November 1942, Rejewski and fellow mathematician Henryk Zygalski fled, via Spain, Portugal and Gibraltar, to Britain. There they worked at a Polish Army unit, solving low-level German ciphers. In 1946 Rejewski returned to his family in Poland and worked as an accountant, remaining silent about his cryptologic work until 1967.