Near Field Communication (NFC) has emerged as a pivotal wireless technology for short-range data exchange between devices, including smartphones and wearables. Leveraging Radio Frequency (RF) signals and robust authentication, NFC ensures secure communication in proximity. Mutual authentication (MA) holds paramount importance for establishing trust between device pairs. A prime example of NFC technology is Radio Frequency Identification (RFID), wherein seamless communication occurs between a reader and a tag. However, security and privacy concerns are critical factors in RFID systems, necessitating effective authentication protocols. This paper introduces an efficient and secure MA mechanism for RFID devices, using lightweight block ciphers (LBCs). Specifically, the extended tiny encryption algorithm (XTEA) and the hummingbird algorithm (HBA) using the cipher block chaining (CBC) mode is designed. These tailored algorithms establish a secure communication channel between RFID tags and readers. Notably, the proposed RFID-MA using XTEA and HBA occupies less than 2% of the chip area, encompassing slices and lookup tables (LUTs), and achieves authentication with execution times of $11.6~\mu \text{s}$ and $1.34~\mu \text{s}$ , respectively. In comparison to the RFID-MA approach employing the XTEA methodology, the proposed algorithm reduces the chip area overhead by 24.6%, total power consumption by 3.5%, and execution time by 88.36%. The proposed algorithm is implemented using Verilog hardware description language (HDL) within the Xilinx environment and is realized on a Artix-7 field programmable gate array (FPGA) platform, utilizing the ModelSim simulator. The proposed research extensively presents simulation and synthesis results while considering the critical hardware constraints such as time, power, and area. Furthermore, this study has also conducted a comprehensive performance analysis, comparing essential metrics with existing LBC and authentication methodologies, showcasing substantial improvements.