High Quality Content by WIKIPEDIA articles! In mathematics, the Weil pairing is a construction of roots of unity by means of functions on an elliptic curve E, in such a way as to constitute a pairing (bilinear form, though with multiplicative notation) on the torsion subgroup of E. The name is for Andre Weil, who gave an abstract algebraic definition; the corresponding results for elliptic functions were known, and can be expressed simply by use of the Weierstrass sigma function. Pairing-based cryptography is the use of a pairing between elements of two groups to a third group to construct cryptographic systems. Usually the same group is used for the first two groups, making the pairing in fact a mapping from two elements from one group to an element from a second group. In this way, pairings can be used to reduce a hard problem in one group to a different, usually easier problem in another group.

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