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This paper presents a performance comparison of newly created matrix power function (MPF) based symmetric cipher realized in cipher-block chaining mode (CBC) with two other standardized ciphers namely AES-128 and triple DES. The encryption rate is compared using 64 bits arithmetic operations. It is shown that the proposed cipher has a significant advantage against compared ciphers. It is achieved by consuming more memory for MPF realization. Mentioned ciphers are compared using the central processing unit (CPU) the number of clock cycles required to encrypt fixed size plaintexts. This paper also includes a comparison of a number of operations required to encrypt plaintext as well as memory requirements for each of the ciphers with pre-determined parameters. The main difference between symmetric cipher based on MPF and other standardized ciphers mentioned in the paper is the ability to work with larger matrix entries in comparison to other algorithms as well as availability to parallelize the process of encrypting a single block.

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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.

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.