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Keywords:
cryptography; lifting scheme; min-max-plus algebra; wavelet
cryptography; lifting scheme; min-max-plus algebra; wavelet
Summary:
We propose a cryptographic algorithm utilizing integer wavelet transform via a lifting scheme. In this research, we construct some predict and update operators within the lifting scheme of wavelet transforms employing operations in min-max-plus algebra, termed as lifting scheme integer wavelet transform over min-max-plus algebra (MMPLS-IWavelet). The analysis and synthesis process on MMPLS-IWavelet is implemented for both encryption and decryption processes. The encryption key comprises a sequence of positive integers, where the first element specifies MMPLS-IWavelet type and subsequent elements indicate the levels of each executed transformation. The decryption key involves three components: the original encryption key, a binary encoding of the analyzed signal, and a sequence of non-negative integer representing the length of coefficient signals from the approximation and detail signals. We present a rigorous analysis confirming the correctness of the proposed cryptographic scheme, and evaluate its performance based on various metrics such as correlation value between plaintext and ciphertext, encryption quality, computation time, key sensitivity, entropy analysis, and key space analysis. We also analyze the computational costs of the encryption and decryption processes. The experimental results demonstrate that the proposed algorithms empirically yield satisfactory performance, exhibiting a near zero correlation between plaintext and ciphertext for most of test data, high encryption quality (over 80 percent), substantial key sensitivity, the large key space, and greater randomness in ciphertext compare to plaintext. The algorithm is efficient in terms of computational time and has linear complexity with respect to the number of input characters. The vast key space makes it highly impractical for brute-force approaches to find the decryption key directly.
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