Internet of Things (IoT) techniques have been employed in many areas, e.g., vehicles, smart home, and medicine. Among the applications of IoTs, the Internet of Vehicles (IoV) is one of the most popular techniques. IoVs are protected by public key cryptographic systems, such as RSA and ECC. However, such systems are vulnerable to quantum computer attacks. Thus, we improve the security of IoV-based post-quantum signatures, which can resist quantum computer attacks. The key operations are divisions in a finite field. Hence, we improve the security of IoV-based post-quantum signatures with division by employing systolic architectures. We propose a systolic architecture for computing division in composite fields. After that, we improve the IoT security-based post-quantum signatures with systolic divisions. We test and verify our design on a Field-Programmable Gate Array (FPGA); the experimental results confirm our estimates. Furthermore, the optimized method proposed can be further applied to various applications like solving system of linear equations and cryptographic applications for IoT security.