Bilinear Pairings on Lemniscates Curve - Jai Arul Jose, G; A. Hussein Al-Nuaimy2, Louay; Mastan, Md (International Journal of Engineering and Technology, 2018)
Â Bilinear pairings, also called bilinear mappings, have developed as an important active area of cryptographic research. The Tate and Weil pairings were proposed for the use of cryptography such as identity-based cryptography, attribute base cryptography, pairing based cryptography, and short signatures. A bilinear pairing is a mapping of a pair of points on an elliptic curve defined on any field F to an element of the multiplicative group of a finite extension of F. Bilinear mappings transfer the discrete logarithm problem from a curve defined over a finite field to the multiplicative group of a finite field. In geometry, Lemniscates curve is aÂ plane curve based on two given points called foci. These foci are located at distance 2a from each other. In this work, bilinear pairings is applied to Lemniscates curve with the model of elliptic curve pairings.Â