Colluding tags attack on the ECC-based grouping proofs for RFIDs

Recently, a new privacy-preserving elliptic curve based grouping proof protocol with colluding tag prevention (CTP) has been proposed. The CTP protocol is claimed to be resistant against colluding tags attacks in which the involved tags can exchange some messages via another reader before the protocol starts without revealing their private keys. In this paper, we show that the CTP protocol is vulnerable to some colluding tag attacking scenario. In addition, we propose a new elliptic curve based grouping protocol which can fix the problem. Our proposal is based on a formally proved privacy preserving authentication protocol and has the advantage of being resistant against colluding tags attacks with the same amount of computation.