1. Home
  2. Issues
  3. Volume 33, Issue 4 (2022)
  4. CBC Mode of MPF Based Shannon Cipher Def ...

Informatica


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.

References

 
Boneh, D., Shoup, V. (2020). A Graduate Course in Applied Cryptography.
 
Grundman, H.G., Smith, T.L. (1996). Automatic realizability of Galois groups of order 16. In: Proceedings of the American Mathematical Society, AMS ’96. AMS, Rhode Island, USA, pp. 2631–2640.
 
Grundman, H.G., Smith, T.L. (2010a). Galois realizability of groups of order 64. Central European Journal of Mathematics, 8(5), 846–854.
 
Grundman, H.G., Smith, T.L. (2010b). Realizability and automatic realizability of Galois groups of order 32. Central European Journal of Mathematics, 8(2), 244–260.
 
Katz, J., Lindell, Y. (2007). Introduction to Modern Cryptography. CRC Press, New York.
 
Levinskas, M., Mihalkovich, A. (2021). Avalanche effect and bit independence criterion of perfectly secure Shannon cipher based on matrix power. Mathematical Models in Engineering, 7(3), 50–53. https://doi.org/10.21595/mme.2021.22234.
 
Michailov, I. (2007). Groups of order 32 as Galois groups. Serdica Mathematical Journal, 33(1), 1–34.
 
Mihalkovich, A. (2018). On the associativity property of MPF over M16. Lietuvos matematikos rinkinys: Lietuvos matematiku draugijos darbai, Serija A, 59, 7–12.
 
Mihalkovich, A., Levinskas, M., Makauskas, P. (2022). MPF based symmetric cipher performance comparison to AES and TDES. Mathematical Models in Engineering, 8(2), 15–25. https://doi.org/10.21595/mme.2022.22517.
 
Mihalkovich, A., Sakalauskas, E., Luksys, K. (2020). Key exchange protocol defined over a non-commuting group based on an NP-complete decisional problem. Symmetry, 12, 1389. https://doi.org/10.3390/sym12091389.
 
Sakalauskas, E., Luksys, K. (2012). Matrix power function and its application to block cipher s-box construction. International Journal of Innovative Computing, Information and Control, 8(4), 2655–2664.
 
Sakalauskas, E., Mihalkovich, A. (2018). MPF problem over modified medial semigroup is NP-complete. Symmetry, 10(11), 571. https://doi.org/10.3390/sym10110571.
 
Sakalauskas, E., Mihalkovich, A., Uselis, A. (2020a). Security analysis of KAP based on enhanced MPF. IET Information Security, 14(4), 410–418.
 
Sakalauskas, E., Dindiene, L., Kilciauskas, A., Luksys, K. (2020b). Perfectly secure Shannon Cipher construction based on the matrix power function. Symmetry, 12, 860. https://doi.org/10.3390/sym12050860.
 
Shannon, C.E. (1949). Communication theory of secrecy systems. The Bell System Technical Journal, 28(4), 656–715.
 
Sylow, M.L. (1872). Théorèmes sur les groupes de substitutions. Mathematische Annalen, 5, 584–594. https://doi.org/10.1007/BF01442913.

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.


Full article Related articles Cited by PDF XML
Full article Related articles Cited by PDF XML

Copyright
© 2022 Vilnius University
Open access article under the CC BY license.

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

Metrics
since January 2020
483

Article info
views

 259

Full article
views
215

PDF
downloads

 85

XML
downloads


Share


RSS