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In this paper, the authors propose an elaborate geometric approach to explain the group law on Jacobi quartic curves which are seen as the intersection of two quadratic surfaces in space. Using the geometry interpretation, they construct the Miller function. Then they present explicit formulae for the addition and doubling steps in Miller's algorithm to compute Tate pairing on Jacobi quartic curves. Both the addition step and doubling step of their formulae for Tate pairing computation on Jacobi curves are faster than previously proposed ones.
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