Anomalous Behaviour of Cryptographic Elliptic Curves over Finite Field

New wireless technologies and approaches enable to connect even the simplest sensors with limited computational power to the global network. The need for efficient and secure solutions is growing with the wider use of these devices. This paper provides a new method for speed optimization of Elliptic Curve Cryptography operations which are frequently used in the light-weight secure communication algorithms. This method is based on the anomalous behaviour of specific elliptic curves. We analyse more than 60 curves of various international standards. Further, our method is less complex, easy to deploy and comparable effective as ordinary, more complex methods. Last but not least, we show the importance of future research in the area of elliptic curve parameterization.