Using the kronecker product of matrices for modification cryptographic algorithm
The article discusses the use of the Kronecker product (KP) to improve the efficiency of cryptographic algorithms. The formation of large matrices with specified properties using KP of small matrices can be used in the development of new block cryptographic algorithms that use matrices with the following properties: orthogonal (unitary), invertible, involutive. Hill cipher modifications with a plaintext key matrix, T = 2<sup>K</sup> bytes, represented as a Kronecker product of К invertible elementary matrices (IEM), are considered in a number of works. They have quadratic computational complexity O(T<sup>2</sup>). We propose modifications of the Hill cipher based on KP where the matrix of keys of a quadratic size is not actually calculated. Instead, IEMs are iteratively multiplied by the plaintext in О (Tlog<sub>2</sub> T) time and need linear memory complexity. The estimation of the encryption time for such modified algorithms is similar to the estimation of the AES and RC4 ciphers.