Tate pairing

For the related pairing on the Tate–Shafarevich group, see Cassels–Tate pairing.

In mathematics, Tate pairing is any of several closely related bilinear pairings involving elliptic curves or abelian varieties, usually over local or finite fields, based on the Tate duality pairings introduced by Tate (1958, 1963) and extended by Lichtenbaum (1969). Rück & Frey (1995) applied the Tate pairing over finite fields to cryptography.

See also

Weil pairing

References

Lichtenbaum, Stephen (1969), "Duality theorems for curves over p-adic fields", Inventiones Mathematicae, 7: 120–136, doi:10.1007/BF01389795, ISSN 0020-9910, MR 0242831
Rück, Hans-Georg; Frey, Gerhard (1994), "A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves", Mathematics of Computation, 62 (206): 865–874, doi:10.2307/2153546, ISSN 0025-5718, MR 1218343
Tate, John (1958), WC-groups over p-adic fields, Séminaire Bourbaki; 10e année: 1957/1958, 13, Paris: Secrétariat Mathématique, MR 0105420
Tate, John (1963), "Duality theorems in Galois cohomology over number fields", Proceedings of the International Congress of Mathematicians (Stockholm, 1962), Djursholm: Inst. Mittag-Leffler, pp. 288–295, MR 0175892

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