Pairings
Let , , and be three cyclic groups of the same order. A map is said to be bilinear if . If a bilinear map is also non-degenerate (meaning, it does not map all pairs in to the identity element ) and is efficiently computable, then is called a pairing. This terminology refers to the fact that associates each pair of elements in to an element of .
In the general case that , the pairing is said to be asymmetric, while the case that is called symmetric. Asymmetric pairings are much more efficient in practice than symmetric pairings.
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