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CBC Mode of MPF Based Shannon Cipher Defined Over a Non-Commuting Platform Group
Volume 33, Issue 4 (2022), pp. 833–856
Pub. online: 9 December 2022      Type: Research Article      Open accessOpen Access
Received
1 May 2022
Accepted
1 November 2022
Published
9 December 2022

Abstract

Commonly modern symmetric encryption schemes (e.g. AES) use rather simple actions repeated many times by defining several rounds to calculate the ciphertext. An idea we previously offered was to trade these multiple repeats for one non-linear operation. Recently we proposed a perfectly secure symmetric encryption scheme based on the matrix power function (MPF). However, the platform group we used was commuting. In this paper, we use a non-commuting group whose cardinality is a power of 2 as a platform for MPF. Due to the convenient cardinality value, our scheme is more suitable for practical implementation. Moreover, due to the non-commuting nature of the platform group, some “natural” constraints on the power matrices arise. We think that this fact complicates the cryptanalysis of our proposal. We demonstrate that the newly defined symmetric cipher possesses are perfectly secure as they were previously done for the commuting platform group. Furthermore, we show that the same secret key can be used multiple times to encrypt several plaintexts without loss of security. Relying on the proven properties we construct the cipher block chaining mode of the initial cipher and show that it can withstand an adaptive chosen plaintext attack.

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Biographies

Mihalkovich Aleksejus
https://orcid.org/0000-0002-8661-3021
aleksejus.michalkovic@ktu.lt

A. Mihalkovich obtained his PhD in 2015 and is currently an assistant professor at Kaunas University of Technology. He is a member of Identification and Cryptography Research Group and performs various investigations in symmetric and asymmetric cryptography.

Levinskas Matas
matas.levinskas@ktu.edu

M. Levinskas is currently pursuing a master’s degree at Kaunas University of Technology. He is a member of Identification and Cryptography Research Group and performs investigations in symmetric cryptography.

Dindiene Lina
lina.dindiene@ktu.lt

L. Dindiene obtained her PhD in 2016 and is currently a lecturer at Kaunas University of Technology. She is a member of Identification and Cryptography Research Group and investigates statistical and probabilistic properties of cryptographic primitives.

Sakalauskas Eligijus
https://orcid.org/0000-0002-4620-4469
eligijus.sakalauskas@ktu.lt

E. Sakalauskas is currently a professor at Kaunas University of Technology. He is the head of Identification and Cryptography Research Group and performs various investigations in symmetric and asymmetric cryptography.


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Open access article under the CC BY license.

Keywords
symmetric cryptography perfect secrecy non-commuting cryptography matrix power function

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