Users of wireless sensor networks face difficulties like key distribution. Also there is a large number of keys saved in them. Thus, they tended to use public key cryptography for identification and key agreement. On the other hand, certificate-based public key cryptography makes use of public key infrastructure (PKI). Clearly implementing PKI requires a large amount of memory computations and communications which are impassible for sensor networks. To solve this problem we can use identity based cryptography (IBC). In this type of cryptography, user’s public identities like their IP or email addresses are used as their public key as a result, there will be no need for PKI. After introduction of pairing based cryptography, this type of cryptography was applicable used. In this paper, we will take a look at how to use pairings on wireless sensor networks.

In public key cryptography, systems based on integer factorization problem are increasing replaced by systems based on discrete logarithm problem (DLP). In fact, Elliptic curve cryptography(ECC) makes the key size much smaller than similar RSA systems do that is why ECC became very popular among cryptography system designers. The designers always need to get to a cryptography system with the smallest key size the highest security. Thus they tend to use hyper elliptic curve in cryptography. In this paper, we will study how to use this type of curves in cryptography.

Also, this study takes a look at these curves’ resistance against algorithms of solving the discrete logarithm problem. Energy consumed for implementation of the scalar multiplication in hyper elliptic curves of the genus g<5 will be analyzed too.