Journal of Advances in Mathematics and Computer Science

The electronic transmission of polling-station reports must keep results confidential during processing, protect them in transit against present and quantum adversaries, and remain available when the network degrades or is attacked. Existing architectures address these requirements separately and statically. This paper proposes the Cognitive Hybrid Cryptosystem (CHC), which combines Ring-LWE-based BFV homomorphic encryption for blind aggregation and threshold decryption, BB84 quantum key distribution with a hybrid post-quantum fallback (ML-KEM-768 + X25519), and a MAPE-K cognitive engine formalised as a constrained Markov decision process. We mathematically model the electoral workflow and the threat model, prove the correctness of the tally, prove with a sub-Gaussian concentration bound that the aggregation noise grows as √n — which makes bootstrapping unnecessary — and derive from a smudging lemma the admissibility condition of secure threshold decryption: 42 bits of noise budget for a statistical distance of 2^-40 per coefficient, and about 58–59 bits for a global distance of 2^-40over all coefficients and decryptions. The reproducible prototype CHC-Vote, whose ML-KEM-768 module passes the official NIST ACVP test vectors, was evaluated on synthetic electoral data with a simulated quantum channel and a simulated network: 50,000 actually encrypted reports, 12,700 active attacks of five types, and five disruption scenarios repeated over 20 seeds and compared with three baselines (two static configurations and a rule-based loop). In these simulations, aggregation is exact at national scale, every tested attack is rejected, and the cognitive engine delivers 100 % of the reports within the 600-s deadline in all scenarios, against 45–63 % for the static configuration under degradation, with a 98.8–99.1 % reduction of mean latency in the worst-case scenario under both admissibility criteria. A simulated election with 50,000 polling stations in 26 provinces yields a result identical to the plaintext tally. These results establish feasibility in simulation; real-world deployment would additionally require a physical QKD link, constant-time implementations and an independent audit.