A unified elliptic curve cryptographic algorithm for secure communication and homomorphic encryption: A multi-parameter (Built-in CIA) Approach

• Rising Importance of Data Security: The increasing volume and complexity of data, along with emerging technologies (e.g., cloud computing and IoT), make data security more critical than ever. • Limitations of Existing Cryptographic Algorithms: Most well-known algorithms mainly provide confidentiality but lack full support for Confidentiality, Integrity, and Authentication (CIA). Signature algorithms are typically required to support integrity and authentication. • Proposed Elliptic Curve-Based Algorithm: A new Elliptic Curve Cryptographic (ECC) algorithm is introduced that supports all CIA parameters within a single algorithm. • Improved TLS/SSL Integration: The algorithm can be used in TLS/SSL protocols to establish secure connections more efficiently, requiring fewer steps. • Performance Optimization Using CRT: By applying the Chinese Remainder Theorem (CRT) and a double-and-add method over elliptic curve point arithmetic (including text-to-point conversion), the algorithm reduces time complexity. • Resistance to Attacks: The proposed algorithm enhances defence against Power Analysis Attacks (PAA) and Side Channel Attacks (SCA). • Support for Secure Data Processing: The algorithm incorporates homomorphic encryption, enabling secure data processing while maintaining privacy. • Superior Performance: It demonstrates better overall performance compared to existing cryptographic methods. Data security is a critical concern due to the increasing volume and complexity of data being generated and processed. Data security involves implementing strategies, protocols, and technologies to safeguard data from unknown access, breaches, and other threats. With the rise of cloud computing, IoT devices, and sophisticated cyber threats, maintaining data security requires a multifaceted approach that adapts to evolving risks and technologies. Cryptographic algorithms are unable to support security parameters as a whole, such as Confidentiality, Integrity, and Authentication(CIA). Major, well-known cryptographic algorithms support only confidentiality; to support other parameters, we need to go for algorithms like signature algorithms. So far, no algorithm supports all security parameters. Here we introduce the Elliptic Curve-based Cryptographic Algorithm with built-in CIA parameters handled in the same algorithm effectively. The Transport Layer Security (TLS/SSL) protocol can also utilize it to establish secure connections between authorized parties in fewer steps. Applying the Chinese Remainder Theorem (CRT)-based double and add method over Elliptic Curve point arithmetic, and text to point conversion are significantly reduced the time complexity of the proposed algorithm, enhancing its resistance against Power Analysis Attack (PAA) and Side Channel Attack (SCA). Additionally, it supported the data security in processing through homomorphic encryption, and demonstrated superior overall performance compared to the current state-of-the-art.