Avalanche effect and bit independence criterion of perfectly secure Shannon cipher based on matrix power

Abstract

In 2020 E. Sakalauskas with coauthors published a paper defining perfectly secure Shannon cipher based on matrix power function, proposing effective parallelization, and ensuring no need for multiple rounds encrypting one data block [1]. In this paper we present computational results with the avalanche effect and bit independence criterion (BIC). These criteria are important when describing the rate of confusion of bits in the ciphertext. It was observed that increasing matrix order and group size enhance BIC and avalanche effect results converging to the desired values. Based on the outputs it is possible to pick appropriate parameters satisfying security needs and available memory in a device where appropriate keys are going to be stored.

Construction of Substitution Boxes Using Finite Fields

“…According to the SAC, a desirable property is achieved when the complementation of a single input bit results in each output bit changing with an equal probability of 50 percent. This criterion, as explained in the work by Levinskas et al [11], provides a quantifiable standard for assessing the effectiveness and strength of cryptographic algorithms in terms of their ability to produce significant changes in output for even minor modifications in input.…”

“…The bit independence criterion (BIC), as outlined in the research by Levinskas et al [11], stipulates that in a cryptographic system, when a single input bit i is inverted, the resulting changes in output bits j and k should occur independently. This criterion emphasizes that there should be no correlation or dependency between the changes in different 'output bits when a single input bit' is modified…”

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

“…Moreover, we evaluated the computational costs of AES and TDES protocols operating in the CBC mode based on the notion of clock cycles. To achieve a balance between the memory requirements, performance, and statistical properties of our scheme, discussed previously in Levinskas and Mihalkovich (2021), we fixed the main parameters of our cipher at m = 4, p = 4079 and q = 2039. Our results have shown that MPF-based CBC mode outperforms AES-128 by 1.5 times and TDES by roughly 47 times.…”