Provable secure lightweight hyper elliptic curve‐based communication system for wireless sensor networks

Abstract

It is widely believed that hyper elliptic curve cryptosystems (HECCs) are not attractive for wireless sensor network because of their complexity compared with systems based on lower genera, especially elliptic curves. Our contribution shows that for low cost security applications HECs cryptosystems can outperform elliptic curve cryptosystems. The aim of this paper is to propose a discrete logarithm problem-based lightweight secure communication system using HEC. We propose this for different genus curves over varied prime fields performing a full scale study of their adaptability to various types of constrained networks. Also, we propose to evaluate the performance of the protocol for computational times with respect to different genus for main operations like Jacobian, Divisor identifications, key generation, signature generation/verification, message encryption, and decryption by changing the size of the field. A formal security model was established based on the hardness of HEC-Decision Diffie-Hellman (HEC-DDH). Finally, a comparative analysis with ECC-based cryptosystems was made, and satisfactory results were obtained. KEYWORDSDiffie-Hellman, elliptic curve, genus, hyper elliptic curve, Jacobian, wireless sensor networks | INTRODUCTIONIn modern world, most of the wireless systems require resource constrained devices such as RFID tags, sensors, smart cards, small processors, PDA's, and smart phones. These devices play a major role in providing security for satellite communication, internet security, e-banking, e-commerce, Internet Of Things (IOT) applications, and embedded systems. Implementing security for wireless communication system using these devices is the most challenging problem. Many cryptographic algorithms were developed to accomplish their requirements for secure data communication in wireless systems. These algorithms have many limitations, which include increased power consumption, communication, and computational complexity with increased processing time. Thus, an efficient cryptographic algorithm that overcomes these limitations is the need of the hour.Public key cryptography (PKC) 1 offers a solution to the above limitations by using 2 different keys known as the public and private keys. The secret (private) key is chosen by the user and is well known only to him. The public key is computed from the private key by using a reversible mathematical process and is made open to all. Both the keys are interoperable on each other and are used for the decryption and encryption processes. As the private key is never revealed, PKC is highly secured unlike symmetric key cryptography. Based on the arithmetic operations, PKC is broadly

A Lightweight and Secured Certificate-Based Proxy Signcryption (CB-PS) Scheme for E-Prescription Systems

“…The is the compressed form of , which contains fewer key and parameters size [13,14]. Equation 1 represents the of genus ⪰ 2 over a finite field .…”

An Efficient and Provably Secure Certificateless Key-Encapsulated Signcryption Scheme for Flying Ad-hoc Network

“…Thus, a new type, the generalization of elliptic curve, called hyperelliptic curve, was proposed [23]. The hyperelliptic curve features security same as that of the elliptic curve, bilinear pairing and RSA; it uses a 80-bit key, identity and certificate size [24], [25]. The hyperelliptic curve is deemed to be a better choice for energy-constrained devices.…”

An Online-Offline Certificateless Signature Scheme for Internet of Health Things

“…Therefore, a new form, the generalization of the elliptic curve, called the hyperelliptic curve was thus suggested [ 19 ]. The hyperelliptic curve offers the same degree of protection as the elliptic curve, bilinear pairing, and RSA using 80-bit keys, identity, and certificate size [ 20 , 21 ]. For energy-constrained IoHT devices, the hyperelliptic curve would be a better option.…”