A cryptographic algorithm using wavelet transforms over max-plus algebra

Cryptography has a role to secure an important information. Until now, many varieties of cryptographic algorithms are available in the literature. In this paper, we propose a cryptographic algorithm based on Type IVa max-plus wavelet transforms (MP-Wavelets). Encryption and decryption algorithms are constructed based on the analysis and synthesis process of Type IVa MP-Wavelets, respectively. The encryption key contains the number of channels in all levels. The encryption key is chosen such that multiplication of the number of channels in all levels is greater than or equal to the number of characters in the Plaintext. The decryption key consists of the encryption key and a sequence generated by the binary encoding of detail components. This guarantees that the decryption key is very difficult to obtain using the brute-force method. The cryptographic process involves only maximization and addition operations as main operations. The experiments and analysis show that the algorithm is a good cryptographic algorithm based on the correlation between Plaintext and Ciphertext, encryption quality, the decryption key space, cryptanalysis (Ciphertext-only attack) and security analysis (entropy analysis, key sensitivity, Plaintext sensitivity). This algorithm is also efficient in the running time, because the complexity is linear w.r.t. the number of characters in the Plaintext.(c) 2020 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).