Conference article

Decrypting the Hill Cipher via a Restricted Search over the Text-Space

Florent Dewez
INRIA, Modal team-project, Lille-Nord Europe research center, France

Valentin Montmirail
Universite Cote dAzur, I3S, CNRS, Nice, France

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Published in: Proceedings of the 2nd International Conference on Historical Cryptology, HistoCrypt 2019, June 23-26, 2019, Mons, Belgium

Linköping Electronic Conference Proceedings 158:2, p. 13-22

NEALT Proceedings Series 37:2, p. 13-22

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Published: 2019-06-12

ISBN: 978-91-7685-087-9

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


Developed by L. S. Hill in 1929, the Hill cipher is a polygraphic substitution cipher based on matrix multiplication. This cipher has been proved vulnerable to many attacks, especially the known-plaintext attack, while only few ciphertext-only attacks have been developed. The aim of our work is to study a new kind of ciphertext-only attack for the Hill cipher which is based on a restricted search over an explicit set of texts, called orbits, and not on a search over the key-space; it is called Orbit-Based Attack (OBA). To explain in a convenient setting this approach, we make use of basic notions from group action theory; we present then in details an algorithm for this attack and finally results from experiments. We demonstrate experimentally that this new method can be efficient in terms of time-execution and can even be faster on average than the classical Brute-Force Attack in the considered settings.


Hill Cipher Group Action Theory Experiments Ciphertext-only Attack


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