Digital image encryption algorithm through unimodular matrix and logistic map using Python

Abstract

Hill Cipher is one of the methods used in Cryptography. In the Hill Cipher algorithm, the key square matrix must have an inverse modulo. One special matrix that definitely has an inverse is the unimodular matrix. The unimodular matrix can be used as a key in an encryption process. The purpose of this research is to show an alternative in securing digital image data. The type of cryptography used is symmetric cryptography. The algorithm presented by generating a unimodular matrix using the Logistic Map. First, to get a unimodular matrix, we use an identity matrix. The sequence of real number in (0,1) of Logistic Map then converted into integer number from 0 to 255. That number then occupies upper triangular entries of the unimodular matrix. We use the Elementary Row Operation to obtain the complete matrix as a key. Then the multiplication of matrix modulo is used as an encryption process. The unimodular matrix generated by the proposed algorithm guarantees a key in the Hill Cipher for all matrix sizes (n > 4) and only need two parameters (password 1 and password 2). We also tested the algorithm in python language on two digital images (grayscale and color) with different sizes. The results show that the encrypted images are very difficult to read by third parties. The time needed is based on password 1, that is the size of the key matrix. So, the unimodular matrix and logistic map work very well with Hill Cipher to encrypt a digital image.