To ensure the security of sensitive data, elliptic curve cryptography (ECC) is adopted as an asymmetric method that balances security and efficiency. Nevertheless, embedding messages into elliptic curve (EC) points poses a significant challenge. The intricacies of this process can greatly affect the overall security and efficiency of the cryptosystem, reflecting security vulnerabilities observed in many existing schemes that utilize ElGamal ECC-based encryption. In this paper, we introduce an innovative hash-based technique for securely embedding messages into EC points before encryption. A random parameter and a shared secret point generated through the EC Diffie–Hellman protocol are used to bolster the scheme’s security. The security of the proposed method is evaluated against various attack models; moreover, the complexity, and sensitivity of the encryption scheme, as well as its inputs, are analyzed. The randomness assessment of the ciphertext was performed using the NIST statistical test suite. Additionally, we propose a mechanism to ensure the integrity of the message by securely appending a tag to the ciphertext. As a consequence, a comprehensive analysis of our scheme demonstrates its effectiveness in maintaining data security and integrity against various attack models. The algorithm also meets more criteria such as the strict avalanche criterion, linear complexity, and operability.

As the Internet of Things (IoT) expands, ensuring secure and efficient image transmission in resource-limited environments has become crucial and important. In this paper, we propose a lightweight image encryption scheme based on Elliptic Curve Cryptography (ECC), tailored for embedded and IoT applications. In this scheme, the image data blocks are mapped into elliptic curve points using a decimal embedding algorithm and shuffled to improve resistance to tampering and noise. Moreover, an OTP-like operation is applied to enhance the security while avoiding expensive point multiplications. The proposed scheme meets privacy and cybersecurity requirements with low computational costs. Classical security metrics such as entropy, correlation, NPCR, UACI, and key sensitivity confirm its strong robustness. Rather than relying solely on direct comparisons with existing benchmarks, we employ rigorous statistical analyses to objectively validate the encryption scheme’s robustness and security. Furthermore, we propose a formal security analysis that demonstrates the resistance of the new scheme to chosen-plaintext attacks and noise and cropping attacks, while the GLCM analysis confirms the visual encryption quality. Our scheme performs the encryption of a $512\times 512$ image in only 0.23 s on a 1 GB RAM virtual machine, showing its efficiency and suitability for real-time IoT systems. Our method can be easily applied to guarantee the security and the protection of lightweight data in future smart environments.

In this paper, we establish a fixed-point theorem for mixed monotone operators in ordered Banach algebras by introducing a novel contraction condition formulated in terms of the product law, which represents a significant departure from the traditional additive approach. By exploiting the underlying algebraic structure, our method ensures both the existence and uniqueness of fixed points under broader conditions. To illustrate the effectiveness of the proposed theorem, we also provide a concrete example that demonstrates its applicability.

In this paper, we present a fast and effective method for Bidimensional Empirical Mode Decomposition (BEMD) of large images. The proposed approach is based on the integration and adaptation of the partition of unity (PU) algorithm with compactly supported radial basis functions (CSRBFs) within the BEMD method. While the traditional BEMD algorithm is computationally intensive due to its reliance on envelope interpolation, the novel approach overcomes this limitation, as demonstrated by both complexity analysis and experimental results. Results obtained from both synthetic and real images demonstrate significant improvements in computational efficiency and decomposition quality compared to the recent BEMD-CSRBF approach, which demonstrates an important advancement over traditional BEMD methods. These improvements are reflected in lower orthogonality index (OI) values and faster processing times compared to the BEMD-CSRBF method. Across the tested images, the proposed BEMD-PU method reduces the computation time by ($17.22\%$)–($69.94\%$) and decreases the OI by ($8.93\%$)–($62.23\%$) compared with BEMD-CSRBF; on average, the computation time and OI are reduced by ($44.76\%$) and ($31.49\%$), respectively. Consequently, the proposed method performs exceptionally well with large images, making it an efficient tool for image processing.