This research addressed the challenge of secure multiplication over encrypted data, where information security and data integrity must be preserved. To this end, we proposed the design and validation of a hybrid quantum – classical model that multiplies encrypted polynomials, a foundational component of the Cheon–Kim–Kim-Song (CKKS) homomorphic encryption, grounded in the Ring Learning With Errors (RLWE) problem. Furthermore, the proposed solution leverages quantum convolutions by Quantum Fourier Transform (QFT), to explore quantum interference and superposition properties within the homomorphically encrypted domain. Methodologically, the model was implemented using the Qiskit framework, integrated with the Microsoft SEAL cryptographic library using the Python programming language. The results demonstrated that the product computed over homomorphically encrypted data corresponds–within a bounded and controlled error margin – to the plaintext product, thereby validating that the integration of quantum techniques into a classical cryptosystem does not compromise data security and preserves algebraic fidelity. Throughout the quantum multiplication process, the data remained unintelligible, accessible exclusively to authorized users. This constitutes a significant and scalable contribution to the development of secure data processing models within quantum environments.

Keywords

Quantum computing, CKKS homomorphic encryption, Quantum multiplication, Data security, Quantum Fourier Transform