(untitled) (Eureka Journal of Computing Science & Digital Innovation, 2026)
This paper studies the modeling of elliptic curve cryptography and isogeny-based algorithms in a quantum computing environment, which play an important role in the post-quantum cryptography paradigm. In the study, the operations of adding and doubling points on an elliptic curve are mathematically analyzed and implemented using the Python programming language. In addition, a quantum scheme based on the Qiskit platform was developed to simulate the quantum computing environment. The model describes a simplified view of the isogeny mapping process using quantum superposition and nonlinear transformations. The proposed model was tested on a local quantum simulator and the results were analyzed using a probability distribution. The results obtained demonstrate the possibility of modeling elliptic curve-based cryptographic algorithms in a quantum environment and provide an important theoretical basis for post-quantum cryptography research.