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Title:
On a Relation between the Ate Pairing and the Weil Pairing for Supersingular Elliptic Curves
Authors: Takakazu Satoh
Abstract:The hyperelliptic curve Ate pairing provides an efficient way to compute a bilinear pairing on the Jacobian variety of a hyperelliptic curve. We prove that, for supersingular elliptic curves with embedding degree two, square of the Ate pairing is nothing but the Weil pairing. Using the formula, we develop an X-coordinate only pairing inversion method. However, the algorithm is still infeasible for cryptographic size problems.
ePrint: https://eprint.iacr.org/2013/532
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