Internet of Things (IoT) is very attractive because of its promises. However, it brings many challenges, mainly issues about privacy preserving and lightweight cryptography. Many schemes have been designed so far but none of them simultaneously takes into account these aspects. In this paper, we propose an efficient ABC scheme for IoT devices. We use ECC without pairing, blind signing and zero knowledge proof. Our scheme supports block signing, selective disclosure and randomization. It provides data minimization and transactions' unlinkability. Our construction is efficient since smaller key size can be used and computing time can be reduced. As a result, it is a suitable solution for IoT devices characterized by three major constraints namely low energy power, small storage capacity and low computing power.