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The emergency of quantum computing is a threat to the foundations of classical cryptographic systems such as RSA and ECC. Currently these algorithms underpin modern data security. Quantum computing based attacks when executed can render these cryptographic systems obsolete. Thus, there is need to transition to quantum-resistant cryptography to protect critical infrastructure including in smart cities where secure and resilient data exchange is paramount. However, this transiting is faced with significant challenges due to legacy systems. To solve this issue, our paper introduces Hybrid Quantum-Safe Encryption (HQSE) that is a dual layer encryption integrating classical cryptography with Quantum computing resistant techniques. Specifically, we evaluate our approach using an integrated classical RSA and Kyber512 that is a lattice based post-quantum algorithm. Multiple files ranging from 256 kb to 2048 kb were then encrypted and decrypted using each algorithm, The performance of our approach was evaluated using metrics such as encryption and decryption time, integrity verification, matching ratio and error rate. Results indicated that Kyber512 consistently outperformed RSA in terms of efficiency. On the other hand, the hybrid model demonstrated middle ground behavior signifying enhanced security without substantial performance loss. Notably our solution achieved near-zero integrity verification delays, matching ratio of 1 and error rate of 0 across all the algorithms. These insights validate the HQSE as a viable transitional solution for protecting legacy cryptographic systems against quantum-era threats. Furthermore, this research contributes to global cybersecurity by introducing a hybrid encryption model that enhances digital resilience particularly in the next generation smart cities.