Rivest, Shamir, & Adleman (RSA), bilinear pairing, and elliptic curve are well-known techniques/algorithms for security protocols. These techniques suffer from higher computation and communication costs due to increased sizes of parameters, public keys, and certificates. Hyper-elliptic curve has lower parameter size, public key size, and certificate size. The aim of the proposed work is to reduce the computational cost and communication cost. Furthermore, we validate the security properties of our proposed scheme by using the well-known simulation tool called automated validation of Internet security protocols and applications. Our approach ensures security properties such as resistance against replay attack, confidentiality, authenticity, unforgeability, integrity, non-repudiation, public verifiability, and forward secrecy.

Security and efficiency remain a serious concern for Internet of Things (IoT) environments due to the resource-constrained nature and wireless communication. Traditional schemes are based on the main mathematical operations, including pairing, pairing-based scalar multiplication, bilinear pairing, exponential operations, elliptic curve scalar multiplication, and point multiplication operations. These traditional operands are cost-intensive and require high computing power and bandwidth overload, thus affecting efficiency. Due to the cost-intensive nature and high resource requirements, traditional approaches are not feasible and are unsuitable for resource-limited IoT devices. Furthermore, the lack of essential security attributes in traditional schemes, such as unforgeability, public verifiability, non-repudiation, forward secrecy, and resistance to denial-of-service attacks, puts data security at high risk. To overcome these challenges, we have introduced a novel signcryption algorithm based on hyperelliptic curve divisor multiplication, which is much faster than other traditional mathematical operations. Hence, the proposed methodology is based on a hyperelliptic curve, due to which it has enhanced security with smaller key sizes that reduce computational complexity by 38.16% and communication complexity by 62.5%, providing a well-balanced solution by utilizing few resources while meeting the security and efficiency requirements of resource-constrained devices. The proposed strategy also involves formal security validation, which provides confidence for the proposed methodology in practical implementations.