In this paper, we propose SEAS, a novel privacy preserving, anonymous authentication scheme for RFID tags, which allows the tags to use pseudonyms instead of their true identity for authentication. Using SEAS, a tag generates random numbers and uses them to create a pseudonym as its identity for authentication. The pseudonym does not reveal the identity of the tag and the pseudonyms of multiple authentications appear random and uncorrelated to the adversary. A pseudonym can only be deciphered by the back-end authentication authority to identify the tag. No other entity in the network can link the pseudonym to the identity of the tag. Our scheme is efficient, with a tag needing to perform only simple operations such as XOR, bits shifting, bits concatenation, and random number generation. We perform security analysis of our scheme to show its effectiveness against different forms of attacks. We also perform comparison of our scheme with existing schemes in terms of efficiency in the use of resources. Our scheme performs effectively, while at the same time being better than the other popular schemes in the literature in terms of cost and computation efficiency.