Most of the Radio Frequency IDentification (RFID) authentication protocols, proposed to preserve security and privacy, are analysed to show that they can not provide security against some passive or active attacks. In this paper, the security of two matrix-based protocols, proposed by Karthikeyan and Nesterenko (KN protocol) and Ramachandra et al. (RRS protocol) that conform to Electronic Product Code Class-1 Generation-2 (EPC Class-1 Gen-2) standard, are investigated. Using the linear relationship of multiplication of matrix and vector, we point out that both protocols can not provide scalability, and they are vulnerable to passive impersonation attack. In addition, both protocols are totally insecure if the adversary can compromise one tag to extract the secrets. A modified lightweight matrix-based authentication protocol is presented, which can resist mainly common attacks on an RFID authentication system including eavesdropping, relay attack, desynchronization attack, impersonation attack and tag tracking attack. The new protocol also has the desirable scalability property and can keep secure under compromising attack.
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