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 $NP$ -complete problem. The obtained results of perfect security on a theoretical level coincide with the $NP$ -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.

The transition to a carbon-neutral society represents one of the most pressing global challenges of the 21st century, requiring a radical transformation in how energy is produced, consumed, and managed. Digitalization has emerged as a pivotal driver in energy transition, offering innovative Pathways to enhance energy efficiency and penetrate renewable energy that should lead to reduced GHG emissions. The aim of the research was to develop a model for the evaluation of digitalization impact on GHG emissions where energy serves as a mediating factor. The data of 27 European Union Member States was employed for the investigation covering the period 2014–2023. Principal Component Analysis was utilized to calculate the composite indicators of digitalization and energy. A comprehensive and systematic analysis of the complex interactions of digitalization, energy and GHG emissions was performed using a path analysis. The findings emphasized the critical role of the rebound effect of digitalization as the advantages associated with energy efficiency and the integration of renewable energy, facilitated by digitalization, are overweighted by increased energy consumption. The research ultimately contributes to a deeper understanding of how digitalization can be measured, guided, and optimized to support sustainable energy and mitigation of climate change.

Publisher: Vilnius University Institute of Data Science and Digital Technologies, Journal: Informatica, Title: CBC Mode of MPF Based Shannon Cipher Defined Over a Non-Commuting Platform Group, Authors: Aleksejus Mihalkovich, Matas Levinskas, Lina Dindiene, Eligijus Sakalauskas , 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.

In our previous study, we proposed a perfectly secure Shannon cipher based on the so-called matrix power function. There we also introduced a concept of single round symmetric encryption, i.e., we used the matrix power function together with some rather simple operations to define a three-step encryption algorithm that needs no additional rounds. Interestingly enough, the newly proposed Shannon cipher possesses the option of parallelization—an important property of efficiently performing calculations using several processors. Relying on our previous proposal, in this study we introduce a concept of a one round block cipher, which can be used to encrypt an arbitrary large message by dividing it into several blocks. In other words, we construct a block cipher operating in cipher block chaining mode on the basis of the previously defined Shannon cipher. Moreover, due to the perfect secrecy property of the original algorithm, we show that our proposal is able to withstand the chosen plaintext attack.

In this paper, we demonstrate a way to generalize learning with errors (LWE) to the family of so-called modular-maximal cyclic groups which are non-commuting. Since the group M2t has two cycles of maximal multiplicative order, we use this fact to construct an accurate criterion for restoring the message bit with overwhelming probability. Furthermore, we implement the original idea by O. Regev in the considered group to gain benefits from the non-commutativity of M2t . Also we prove that using this approach we can achieve a level of security comparable to the original idea.