With the advancement of quantum computing, conventional cryptographic approaches are losing strength against possible attacks, showing the necessity of secure alternatives such as lattice-based cryptography, especially for block chain and IoT implementations. Although lattice-based cryptography provides strong quantum resistance, its practical application is hindered by high computational overhead, intricate key management, and power consumption in resource-constrained IoT devices. Additionally, using it in block chain demands secure signature schemes and authentication protocols without compromising performance. Existing solutions compromise between security and efficiency at the expense of power consumption and higher latency. In an effort to solve these challenges, we present a more robust lattice-based cryptographic scheme that enhances aggregate signatures for low communication overhead without compromising security. Our solution also provides a light-weight key exchange mechanism specific to IoT devices, enhancing scalability and energy consumption. Adaptive security elements are also included to counter potential post-quantum threats. Performance tests indicate that our framework substantially minimizes computational complexity while improving security compared to currently available alternatives. The findings attest to its capability to secure block chain-based IoT networks while providing efficient cryptographic operations. By overcoming the major shortcomings of lattice-based cryptography, our research provides a scalable, quantum-resistant solution for IoT and block chain application security in the post-quantum age.