An Efficient and Secure Cryptographic Algorithm Using Elliptic Curves and Max-Plus Algebra-Based Wavelet Transform

Abstract

With the advent of communication networks, protecting data from security threats has become increasingly important. To address this issue, we present a new text encryption scheme that uses a combination of elliptic curve cryptography and max-plus algebra-based wavelet transform to provide enhanced security and efficiency. The proposed encryption process consists of three main phases. In the first phase, the plaintext is encoded using ASCII characters, followed by the introduction of diffusion in its representation. In the second phase, points are computed on an elliptic curve, and a mapping method is applied to introduce randomness into the data. Finally, in the third phase, the output is decomposed using a max-plus algebra-based wavelet transform to generate the ciphertext. We conduct a comprehensive security analysis of our scheme that includes NIST analysis, entropy analysis, correlation analysis, key space, key sensitivity, plaintext sensitivity, encryption quality, ciphertext-only attack, known-plaintext attack, chosen-plaintext attack, and chosen-ciphertext attack. The findings indicate that the proposed scheme exhibits excellent encryption quality, surpassing a value of 76, which is closer to the ideal value. Moreover, the sensitivity of the plaintext is greater than 91%, indicating its high sensitivity. The correlation between the plaintext and ciphertext is very close to the ideal value of zero. The encrypted texts exhibit a high level of randomness and meet the necessary criteria for a strong key space. These characteristics contribute to its superior security, providing protection against various cryptographic attacks. Additionally, the encryption process for a 5995-character plaintext only takes 0.047 s, while decryption requires 0.038 s. Our results indicate that the proposed scheme offers high levels of security while maintaining reasonable computational efficiency. Thus, it is suitable for secure text communication in various applications. Moreover, when compared with other state-of-the-art text encryption methods, our proposed scheme exhibits better resistance to modern cryptanalysis.