  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%.
