Sybil attack consists to generate several false identities in order to bypass access control and thus produce false messages to seriously undermine the normal operation of Wireless Sensor Networks (WSN). It is considered one of the major threats to WSNs. The problem has been widely taken into account by researchers. However, detecting this attack and effectively countering it in the context of resource-constrained connected objects remains a challenge. In this paper, we propose a lightweight authentication system based on elliptic curve cryptography to counter this attack. This asymmetric encryption system uses smaller encryption keys than RSA and EL-Gamal, but offers the same level of security.