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

Aleksejus Mihalkovich (), Matas Levinskas and Eligijus Sakalauskas
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Aleksejus Mihalkovich: Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
Matas Levinskas: Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania
Eligijus Sakalauskas: Faculty of Mathematics and Natural Sciences, Kaunas University of Technology, 44249 Kaunas, Lithuania

Mathematics, 2022, vol. 10, issue 18, 1-17

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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