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Perfectly Secure Shannon Cipher Construction Based on the Matrix Power Function

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Department of Applied Mathematics, Kaunas University of Technology, 44249 Kaunas, Lithuania
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Department of Informatics, Kauno kolegija/University of Applied Science, 50468 Kaunas, Lithuania
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 860; https://doi.org/10.3390/sym12050860
Received: 1 April 2020 / Revised: 30 April 2020 / Accepted: 6 May 2020 / Published: 23 May 2020
A Shannon cipher can be used as a building block for the block cipher construction if it is considered as one data block cipher. It has been proved that a Shannon cipher based on a matrix power function (MPF) is perfectly secure. This property was obtained by the special selection of algebraic structures to define the MPF. In an earlier paper we demonstrated, that certain MPF can be treated as a conjectured one-way function. This property is important since finding the inverse of a one-way function is related to an N P -complete problem. The obtained results of perfect security on a theoretical level coincide with the N P -completeness notion due to the well known Yao theorem. The proposed cipher does not need multiple rounds for the encryption of one data block and hence can be effectively parallelized since operations with matrices allow this effective parallelization. View Full-Text
Keywords: Shannon cipher; symmetric encryption; perfect security; block cipher Shannon cipher; symmetric encryption; perfect security; block cipher
MDPI and ACS Style

Sakalauskas, E.; Dindienė, L.; Kilčiauskas, A.; Lukšys, K. Perfectly Secure Shannon Cipher Construction Based on the Matrix Power Function. Symmetry 2020, 12, 860.

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