Elliptic Public Key Cryptosystem Using DHK and Partial Reduction Modulo Techniques
S.Sheeba Rani Gnanamalar, V. Gomathy, A. Anie Selva Jothi, Thangaraj Kesavan · SSRN Electronic Journal · 2018
This work describes a low-cost Public key Cryptography (PKC) based solution for security services such as authentication as required for wireless sensor networks. It is a software approach using Elliptic Curve Cryptography (ECC) over GF (2m) in order to obtain stronger cryptography using Koblitz curves and TNAF ( τ- adic non-adjacent form) with partial reduction modulo. A Diffie-Hellman key exchange is also implemented between two participants in the network. The mathematics of elliptic curves and how points upon them form an additive abelian group to use these groups for cryptographic purposes, results for the group formed by an elliptic curve over a finite field, E(Fq). We examine the mathematics behind the group of torsion points, to which every point in E(Fq) belongs, to along with a number of other useful results. We finish by describing how to define a discrete logarithm problem using E(Fq) and showing how this can form public key cryptographic systems for use in both encryption and key exchanges. ECC’s uses with smaller keys to provide high security and high speed in a low bandwidth.