The rapid growth of cloud computing and Internet of Things (IoT) applications faces several threats, such as latency, security, network failure, and performance. These issues are solved with the development of fog computing, which brings storage and computation closer to IoT-devices. However, there are several challenges faced by security designers, engineers, and researchers to secure this environment. To ensure the confidentiality of data that passes between the connected devices, digital signature protocols have been applied to the authentication of identities and messages. However, in the traditional method, a user's private key is directly stored on IoTs, so the private key may be disclosed under various malicious attacks. Furthermore, these methods require a lot of energy, which drains the resources of IoT-devices. A signature scheme based on the elliptic curve digital signature algorithm (ECDSA) is proposed in this paper to improve the security of the private key and the time taken for key-pair generation. ECDSA security is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP), which allows one to use much smaller groups. Smaller group sizes directly translate into shorter signatures, which is a crucial feature in settings where communication bandwidth is limited, or data transfer consumes a large amount of energy. The efficiency and effectiveness of ECDSA in the IoT environment are validated by experimental evaluation and comparison analysis. The results indicate that, in comparison to the two-party ECDSA and RSA, the proposed ECDSA decreases computation time by 65% and 87%, respectively. Additionally, as compared to two-party ECDSA and RSA, respectively, it reduces energy consumption by 77% and 82%.