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#(Alternating) <math>e_m(P, P) = 1</math>.
Also, <math>e_m</math> can be computed efficiently.<ref>{{Cite journal |citeseerx = 10.1.1.88.8848|title = Improved Weil and Tate pairings for elliptic and hyperelliptic curves|url = https://archive.org/details/arxiv-math0311391|pages = 169–183|year = 2004|bibcode = 2003math.....11391E|last1 = Eisentraeger|first1 = Kirsten|last2 = Lauter|first2 = Kristin|last3 = Montgomery|first3 = Peter L.|arxiv = math/0311391}}</ref>
===Homomorphic signatures===
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