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

Matas Levinskas,Aleksejus Mihalkovich

doi:10.21595/mme.2021.22234

Matas Levinskas, Aleksejus Mihalkovich

Open Access

https://doi.org/10.21595/mme.2021.22234

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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.

Highlights

The matrix power function (MPF) was introduced in [5], as the following mapping acting on the Cartesian product of the space of square matrices of order m with itself: Mat (R) × Mat (S) × Mat (R) ↦ Mat (S)
Sakalauskas with co-authors used the MPF in 2020 to propose a perfectly secure Shannon cipher defined over Z [1]
In this paper we investigate the avalanche effect and bit independence criterion (BIC) for the presented block cipher in a more general form i.e., we expand the cardinalities of the algebraic structures considered

Summary

Avalanche effect and BIC

Cryptography security analysis methods such as avalanche effect and BIC allow us to evaluate block cipher secrecy by computing elements confusion after changing just one bit [2], determine elements confusion and dependance from other elements [3, 4]. The values of these criteria are commonly calculated by considering the avalanche vector A , which describes ciphertext bits change after flipping one bit in the plaintext:. The bit independence of the two entries is being calculated by the maximal absolute correlation coefficient between avalanche vector j and k components. The value of BIC should be close to 0 ensuring that all the bit changes occur statistically independently

Perfectly secure Shannon cipher based on matrix power function

Computational results

Conclusions