Let $E$ be a supersingular elliptic curve which is defined over $\mathbb{F}_q$ and $P\in E$. Then there exist a distortion map with respect to $P$. I am looking for an algorithm which finds the map and the complexity of the algorithm.
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The paper "Easy Decision-Diffie-Hellman Groups" by S. Galbraith and V. Rotger contains such an algorithm, which requires a polynomial number of operations.
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$\begingroup$ That algorithm constructs an elliptic curve together with a distortion map. The question asks about finding a distortion map for a given curve, which is usually much more difficult. $\endgroup$– yyyyyyyFeb 18 at 3:57