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This work presents an ultra-lightweight, cryptographic, mutual authentication protocol for radio-frequency identification (RFID) tags. The proposed scheme is more secure than its predecessors. The vulnerabilities of previous schemes based on triangular functions and rotation have been demonstrated in traditional and rotational cryptanalysis. In this paper, we summarize the successful attacks on previous schemes and demonstrate further attacks on 3 recent ultra-lightweight protocols. Next, wedoi:10.3906/elk-1212-95 fatcat:dsioh6hpuzcs5g3lx6rnga4dy4