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

Florent Dewez 1 Valentin Montmirail 2 
1 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : 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.
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Submitted on : Monday, August 26, 2019 - 5:39:00 PM
Last modification on : Saturday, June 25, 2022 - 11:39:40 PM
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  • HAL Id : hal-02271395, version 1



Florent Dewez, Valentin Montmirail. Decrypting the Hill Cipher via a Restricted Search over the Text-Space. Linköping Electronic Conference Proceedings, Linköping University Electronic Press, Linköpings universitet, 2019. ⟨hal-02271395⟩



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