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In recent years there has been much interest in the development and the fast computation of bilinear pairings due to their practical and myriad applications in cryptography. Well-known efficient examples are the Weil and Tate pairings and their variants such as the Eta and Ate pairings on the Jacobians of (hyper-) elliptic curves. In this paper, the authors consider the use of projective coordinates for pairing computations on genus 2 hyperelliptic curves over prime fields. They generalize Chatterjee et. al.'s idea of encapsulating the computation of the line function with the group operations to genus 2 hyperelliptic curves, and derive new explicit formulae for the group operations in projective and new coordinates in the context of pairing computations.
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