## 5 Discussion
It is quite important that these gains are achieved without adding any modifications to the TPM architecture or increasing the amount of exchanged data (not counting the results from the less complicated machines, like those presented in Sections 4.1.1 and 4.2.1), preserving compatibility with existing QKD protocols. This compatibility, combined with enhanced security under realistic adversarial conditions, suggests that dynamic update rule selection is a viable enhancement to existing QKD error correction protocols. Future studies on the dynamic approaches to TPM synchronization in the context of cryptography applications should include a broader data set (e.g., more populated or expanded sets of parameters' values) or should be based on some specific list of TPM parameters-either already used in the QKD process, or some recommended values (like those proposed in [46]). The additional expansion of the research could explore integration into live QKD networks and further optimization of selection criteria to balance security and synchronization speed (e.g., integrating multiple approaches to leverage their respective strenghts while simultaneously mitigating the limitations and risks associated with using individual soltions in isolation), comparison of dynamic_rows and dynamic_matrix with other, less popular update rules (such as selective update rule based on entropy, error-corrective update rule which updates weights only when the outputs differ, weight-decaying update rule, or standard rule with additional decaying factor) or even testing the proposed solutions with novel approaches, such as synchronization with non-binary input vectors [47]. Additionally, we do recognize that the attacker may somehow obtain the information on how the victims choose their update rule on each iteration, so it would be worth comparing the performance of synchronization (in the means of number of updates required to synchronize the key, number of attacker updates or attacker's synchronization percentage) in the scenario where all parties use 'dynamic' approaches, compared to standard update rules scenarios. Conceptualization: B.G. and M.N. ; methodology: B.G. and M.N. ; software: B.G. ; validation: B.G. ; formal analysis: B.G. ; investigation: B.G. and M.N. ; resources: B.G. ; data curation: B.G. ; writing--original draft preparation: B.G. and M.N. ; writing--review and editing: B.G., M.M., and M.N. ; visualization: B.G. ; supervision: M.M. and M.N. ; project administration: M.N. ; funding acquisition: M.N. All authors have read and agreed to the published version of the manuscript. This research project was partly supported by the program \"Excellence initiative--research university\" for the AGH University of Krakow. This research was also supported by the National Research Institute, grant number POIR.04.02.00-00-D008/20-01 on \"National Laboratory for Advanced 5G Research\" (acronym PL-5G) as part of the Measure 4.2 Development of modern research infrastructure of the science sector 2014-2020 financed by the European Regional Development Fund and by the EU Horizon Europe Framework Program under grant agreement no. 101119547 (PQREACT). This work was also supported by the Federal Ministry of Education and Science of Bosnia and Herzegovina within the project \"Virtual Quantum Cryptographic Networks\". Not applicable. The results, as well as the source codes for the software used during the research, are available in a GitHub repository, under following link: [[https://github.com/bgdowski-agh/dynamic_TPM_update](https://github.com/bgdowski-agh/dynamic_TPM_update)]([https://github.com/bgdowski-agh/dynamic_TPM_update](https://github.com/bgdowski-agh/dynamic_TPM_update)) (accessed on 4 July 2025). The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.