Tate pairing
{{for|the related pairing on the Tate–Shafarevich group|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 {{harvs|txt|last=Tate|authorlink=John Tate (mathematician)|year1=1958|year2=1963}} and extended by {{harvtxt|Lichtenbaum|1969}}. {{harvtxt|Rück|Frey|1994}} applied the Tate pairing over finite fields to cryptography.
See also
References
- {{Citation | last1=Lichtenbaum | first1=Stephen |authorlink=Stephen Lichtenbaum| title=Duality theorems for curves over p-adic fields | doi=10.1007/BF01389795 |mr=0242831 | year=1969 | journal=Inventiones Mathematicae | issn=0020-9910 | volume=7 | issue=2 | pages=120–136| bibcode=1969InMat...7..120L | s2cid=122239828 }}
- {{Citation | last1=Rück | first1=Hans-Georg | last2=Frey | first2=Gerhard | title=A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves | doi=10.2307/2153546 |mr=1218343 | year=1994 | journal=Mathematics of Computation | issn=0025-5718 | volume=62 | issue=206 | pages=865–874| jstor=2153546 }}
- {{Citation | last1=Tate | first1=John | author1-link=John Tate (mathematician) | title=WC-groups over p-adic fields | url=http://www.numdam.org/item?id=SB_1956-1958__4__265_0 | publisher=Secrétariat Mathématique | location=Paris | series=Séminaire Bourbaki; 10e année: 1957/1958 |mr=0105420 | year=1958 | volume=13}}
- {{Citation | last1=Tate | first1=John | author1-link=John Tate (mathematician) | title=Proceedings of the International Congress of Mathematicians (Stockholm, 1962) | chapter-url=http://mathunion.org/ICM/ICM1962.1/ | publisher=Inst. Mittag-Leffler | location=Djursholm | mr=0175892 | year=1963 | chapter=Duality theorems in Galois cohomology over number fields | pages=288–295 | url-status=dead | archiveurl=https://web.archive.org/web/20110717144510/http://mathunion.org/ICM/ICM1962.1/ | archivedate=2011-07-17 }}
Category:Pairing-based cryptography
Category:Elliptic curve cryptography
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