In many fields, multiple RFID tags are often combined into a group to identify an object. An RFID grouping-proof protocol is\nutilized to prove the simultaneous existence of a group of tags. However, many current grouping-proof protocols cannot simultaneously\nprovide privacy preserving, forward security, and the authentication between reader/verifier and tags, which are\nvulnerable to trace attack, privacy leakage, and desynchronization attack. To improve the secure performance of the current\ngrouping-proof protocols, we propose two provable lightweight grouping-proof protocols that provide forward security, identity\nauthentication, and privacy preserving. Our protocols involve a trusted reader and an untrusted reader, respectively. In order to\navoid verifying some invalid evidences, our protocols complete the authentication of the verifier to the trusted reader and the\nverified tags before the verifier verifies the grouping-proof evidence. Each tag uses parallel mode to complete its signature to\nimprove the efficiency of the protocols. Moreover, the activate-sleep mechanism and the filtering operation are proposed to\neffectively reduce the collision probability and computing load of tags. Our protocols complete the authentication to tags twice by\na verifier and a trusted reader, respectively. They can resist various attacks such as eavesdropping, replay, trace, and\ndesynchronization. The protocols are proven to be secure, flexible, and efficient. They only utilize some lightweight operations.\nTherefore, they are very suitable to the low-cost RFID systems.
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