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Article History

Received: 23 April 2025

Accepted: 12 September 2025

First Online: 29 September 2025

Declarations

:

: This research is a theoretical study in cryptography and does not involve human participants, biological samples, animal experiments, or clinical trials. As such, ethical approval from an institutional review board or ethics committee is not applicable. All analyses and constructions are based on mathematical models and lattice-based cryptographic primitives without ethical implications. This work exclusively involves theoretical algorithm design and mathematical proofs. No human subjects, personal data, or biological materials were utilized in the study. Therefore, informed consent to participate is not required.

: The manuscript contains no personally identifiable data, clinical case studies, or individual-level information. All results are presented as mathematical theorems, cryptographic schemes, and performance comparisons. Consent for publication is not applicable.

: The authors declare no competing interests.