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 (1994) applied the Tate pairing over finite fields to cryptography.

See also

  • Lichtenbaum, Stephen (1969), "Duality theorems for curves over p-adic fields", Inventiones Mathematicae, 7 (2): 120–136, Bibcode:, doi:, ISSN , MR , S2CID
  • 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:, ISSN , JSTOR , MR
  • Tate, John (1958), , Séminaire Bourbaki; 10e année: 1957/1958, vol. 13, Paris: Secrétariat Mathématique, MR
  • Tate, John (1963), , Proceedings of the International Congress of Mathematicians (Stockholm, 1962), Djursholm: Inst. Mittag-Leffler, pp. 288–295, MR , archived from on 2011-07-17