Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group

Mihalkovich, Aleksejus; Levinskas, Matas; Sakalauskas, Eligijus

doi:10.3390/math10183363

Open AccessArticle

Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group

by

Aleksejus Mihalkovich

^*,†

,

Matas Levinskas

^† and

Eligijus Sakalauskas

^†

Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Mathematics 2022, 10(18), 3363; https://doi.org/10.3390/math10183363

Submission received: 5 July 2022 / Revised: 29 August 2022 / Accepted: 13 September 2022 / Published: 16 September 2022

(This article belongs to the Special Issue Recent Advances in Security, Privacy, and Applied Cryptography)

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Abstract

In this paper, we present a counter mode of a Shannon block cipher based on the matrix power function. We make use of the matrix power function to define a single round symmetric cipher. Continuing our previous research, we implement a non-commuting group the order of which is a power of two in order to define a CTR mode in its most classic interpretation. We explore the security of the newly defined scheme, first, by showing that our block cipher is perfectly secure and does not leak any information about the initial plaintext based on the ciphertext. Then, we define a sequence of security games that show how the CTR mode of our cipher can resist all passive attacks.

Keywords: counter mode; symmetric cryptography; perfect secrecy

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MDPI and ACS Style

Mihalkovich, A.; Levinskas, M.; Sakalauskas, E. Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group. Mathematics 2022, 10, 3363. https://doi.org/10.3390/math10183363

AMA Style

Mihalkovich A, Levinskas M, Sakalauskas E. Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group. Mathematics. 2022; 10(18):3363. https://doi.org/10.3390/math10183363

Chicago/Turabian Style

Mihalkovich, Aleksejus, Matas Levinskas, and Eligijus Sakalauskas. 2022. "Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group" Mathematics 10, no. 18: 3363. https://doi.org/10.3390/math10183363

APA Style

Mihalkovich, A., Levinskas, M., & Sakalauskas, E. (2022). Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group. Mathematics, 10(18), 3363. https://doi.org/10.3390/math10183363

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Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group

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