Paper 2023/1874

Security Analysis of an Image Encryption Based on the Kronecker Xor Product, the Hill Cipher and the Sigmoid Logistic Map

Abstract

In 2023, Mfungo et al. introduce an image encryption scheme that employs the Kronecker xor product, the Hill cipher and a chaotic map. Their proposal uses the chaotic map to dynamically generate two out of the three secret keys employed by their scheme. Note that both keys are dependent on the size of the original image, while the Hill key is static. Despite the authors' assertion that their proposal offers sufficient security ($149$ bits) for transmitting color images over unsecured channels, we found that this is not accurate. To support our claim, we present a chosen plaintext attack that requires $2$ oracle queries and has a worse case complexity of $\mathcal O(2^{32})$. Note that in this case Mfungo et al.'s scheme has a complexity of $\mathcal O(2^{33})$, and thus our attack is two times faster than an encryption. The reason why this attack is viable is that the two keys remain unchanged for different plaintext images of the same size, while the Hill key remains unaltered for all images.