CBC Mode of MPF Based Shannon Cipher Defined Over a Non-Commuting Platform Group

• Published in: Informatica (Vilnius, Lithuania) Vol. 33; no. 4; pp. 833 - 856
• Main Authors: Mihalkovich, Aleksejus, Levinskas, Matas, Dindiene, Lina, Sakalauskas, Eligijus
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2022; IOS Press BV
• Subjects: Algorithms; Commuting; Cryptography; Encryption; Mathematical analysis; perfect secrecy; symmetric cryptography; non-commuting cryptography; matrix power function
• ISSN: 0868-4952; 1822-8844; 1822-8844
• DOI: 10.15388/22-INFOR499

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.