Elliptic curve cryptography (ECC) has become a central pillar of modern security due to its efficiency and high level of security provided per bit. However, traditional implementations face challenges in resource-constrained environments, such as IoT devices and wireless sensor networks, due to high computational demands and vulnerabilities to advanced attacks. This paper proposes an innovative extension of ECC, using elliptic curves defined on particular spaces to address these limitations . By generalizing the classical elliptic curve equation with a space-dependent function f(x, y), we optimize the density of valid points and improve computational efficiency, while maintaining security properties. Experimental results show a 15% reduction in execution time for scalar multiplication and a 12% decrease in energy consumption compared to traditional ECC. The proposed method also demonstrates increased resistance to brute force and side-channel attacks, due to the complexity introduced by the function f(x, y). Scalability tests confirm the applicability of the solution in large networks, making it suitable for industrial and critical infrastructures. This work provides a solid theoretical basis and practical validation for the integration of particular spaces in ECC, opening new perspectives for efficient and secure cryptographic solutions. Future research directions include exploring other types of particular spaces, hybridizing with post-quantum cryptographic schemes, and testing the methodology in blockchain and other distributed systems.