In this paper, we propose a novel zero knowledge grouping proof protocol for RFID Systems. Over the years, several protocols have been proposed in this area but they are either found to be vulnerable to certain attacks or do not comply with the EPC Class 1 Gen 2 (C1G2) standard because they use hash functions or other complex encryption schemes. Also, the unique design requirements of grouping proofs have not been fully addressed by many. Our protocol addresses these important security and design gaps in grouping proofs. We present a novel approach based on pseudo random squares and quadratic residuosity to realize a zero knowledge system. Tag operations are limited to functions such as modulo (MOD), exclusive-or (XOR) and 128 bit Pseudo Random Number Generators (PRNG). These can be easily implemented on passive tags and hence achieves compliance with the EPC Global standard while meeting the security requirements.