Summary: The concept of grouping proofs has been introduced by Juels to permit RFID tags to generate a verifiable proof that they have been scanned simultaneously, even when readers or tags are potentially untrusted. In this paper, we extend this concept and propose a narrow-strong privacy-preserving RFID grouping proof and demonstrate that it can easily be extended to use cases with more than two tags, without any additional cost for an RFID tag. Our protocols rely exclusively on the use of Elliptic Curve Cryptography (ECC). To illustrate the implementation feasibility of our proposed solutions, we present a novel ECC hardware architecture designed for RFID.