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Because of simplicity, low cost, and convenience of use, radio frequency identification (RFID) is gaining popularity in a wide variety of applications. At the same time, the threats that RFID systems are susceptible to are also evolving. The practical deployment of RFID systems depends highly on effective security mechanisms that can mitigate numerous intrusions. Providing security in the RFID system is challenging because of its limited power and computational capabilities. Mitigating denial-of-service attacks and providing bi-directional authentication to the tag and reader are the two of the most challenging security issues in RFID systems. In this regard, Karthikeyan and Nesterenko have proposed a matrix-based security protocol that uses simple matrix-based operations and is lightweight in nature. However, their protocol is proven to be vulnerable to de-synchronization and replay attacks. In this paper, we propose a modified matrix-based security protocol that can prevent de-synchronization and replay attacks yet providing a lightweight and effective security mechanism. The proposed protocol can be implemented on the hardware. A practical deployment of the proposed protocol is also feasible.