Conference article

Dawn of Mathematical Cryptology: Probabilists vs Algebraists; Algebraists & Probabilists?

Marek Grajek
Freelance consultant and historian, Poland

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Published in: Proceedings of the 3rd International Conference on Historical Cryptology HistoCrypt 2020

Linköping Electronic Conference Proceedings 171:10, p. 70-76

NEALT Proceedings Series 44:10, p. 70-76

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Published: 2020-05-19

ISBN: 978-91-7929-827-2

ISSN: 1650-3686 (print), 1650-3740 (online)


Traditional cryptology, before the advent of the ciphering machines, relied mostly on the linguistical methods, and the role of mathematics in the codebreaking was limited to counting the frequency of letters, their pairs and triplets. Machine cryptology changed everything; only mathematicians were able to interpret even the bare numbers of combinations resulting from the use of the ciphering machine. The first successful application of advanced mathematics in cryptology, Marian Rejewski’s success with Enigma, marked a change of paradigm; his attack was based on the algebra and the group theory. However, soon after the outbreak of WW2 the Germans had changed the Enigma operational procedures, rendering most Polish methods of attack ineffective. British mathematicians, who took over from the Poles at that moment, had to revert to the old and proven methods based on probability and statistics, which dominated their work during, and well after WW2. This paper presents the early period of the development of the mathematical cryptology, focusing on the clash of two approaches to the codebreaking; that based on statistics and probability on the one side, and algebraic methods on the other.


Enigma; mathematical cryptology; algebraists; probabilists


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