A self-pairing is a pairing computation where both inputs are the same group element.
Self-pairings are used in some cryptographic schemes and protocols.
In this paper, we show how to compute the Tate–Lichtenbaum pairing
on a curve more efficiently than the general case.
The speedup is obtained by using a simpler final exponentiation.
We also discuss how to use this pairing in cryptographic applications.
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