In recent years, the exponentially increasing number of portable wireless devices has made it infeasible to authenticate each individual device of a group separately. With the current trend, the proliferation of devices in the future is said to accelerate further. Therefore, there is an urgent need for a reliable and secure authentication scheme that authenticates a group of devices at once. This paper introduces a concept of group authentication which circumvents the need for individual authentication between a group of devices. Specifically, all the devices which are a member of the group are authenticated at once. Furthermore, the paper proposes a group authentication scheme using Paillier threshold cryptography which is a public key variant of the (t, n) threshold scheme. The proposed scheme is used to verify the authenticity of all the members taking part in a group oriented application. The scheme also helps in establishing a shared secret key between the members of the group which can be used for further communication in any group oriented applications.