Tate pairing

In mathematics, Tate pairing is any of 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.

References

• Lichtenbaum, Stephen (1969), "Duality theorems for curves over p-adic fields", Inventiones Mathematicae 7: 120–136, doi:10.1007/BF01389795, ISSN 0020-9910, MR0242831 
• 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, MR1218343, http://dx.doi.org/10.2307/2153546 
• Tate, John (1958), WC-groups over p-adic fields, Séminaire Bourbaki; 10e année: 1957/1958, 13, Paris: Secrétariat Mathématique, MR0105420, http://www.numdam.org/item?id=SB_1956-1958__4__265_0 
• 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, MR0175892, http://mathunion.org/ICM/ICM1962.1/