J. [. Artin and . Tate, Class Field Theory, 1967.
DOI : 10.1090/chel/366

A. [. Cassels and . Fröhlich, Algebraic Number Theory, 1967.

H. Cohen, Advanced Topics in Computational Number Theory, 2000.

M. [. Fried and . Jarden, Field Arithmetic, 1986.
DOI : 10.1007/978-3-662-07216-5

G. Gras, Class Field Theory. From Theory to Practice, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00259968

M. J. Greenberg, An Elementary Proof of the Kronecker-Weber Theorem, The American Mathematical Monthly, vol.81, issue.6, pp.601-607, 1974.
DOI : 10.2307/2319208

]. H. Has35 and . Hasse, Theorie der relativ-zyklischen algebraischen Funktionenkörper, insbesondere bei endlichem Konstantenkörper, J. reine angew. Math, vol.172, pp.37-54, 1935.

S. [. Hess, M. Pauli, and . Pohst, Computing the multiplicative group of residue class rings, Mathematics of Computation, vol.72, issue.243, pp.1531-1548, 2003.
DOI : 10.1090/S0025-5718-03-01474-1

G. J. Janusz, Algebraic Number Fields, 1973.
DOI : 10.1090/gsm/007

S. Lang, Algebraic Number Theory, 1970.

]. S. Lan73 and . Lang, Elliptic Functions, 1973.

J. S. Milne, Arithmetic Duality Theorems. BookSurge, LLC, second edition, 2006.

J. Neukirch, Algebraic Number Theory, 1999.
DOI : 10.1007/978-3-662-03983-0

J. Neukirch, A. Schmidt, and K. Wingberg, Cohomology of Number Fields, 2008.
DOI : 10.1007/978-3-540-37889-1

]. P. Roq02 and . Roquette, Class field theory in characteristic p, its origin and development, The Proceedings of the International Conference on Class Field Theory, 2002.

M. Rosen, Number Theory in Function Fields, 2002.
DOI : 10.1007/978-1-4757-6046-0

]. H. Sch37 and . Schmid, Zur Arithmetik der zyklischen p-Körper, J. reine angew. Math, vol.176, pp.161-167, 1937.

]. Ser79 and . Serre, Local Fields, 1979.

]. Ser88 and . Serre, Algebraic Groups and Class Fields, Sti93] H. Stichtenoth. Algebraic Function Fields and Codes, 1988.

]. G. Vil06, . Villa, and . Salvador, Topics in the Theory of Algebraic Function Fields, 2006.

]. A. Wei73 and . Weil, Basic Number Theory, 1973.

]. E. Wit35 and . Witt, Der Existenzsatz für abelsche Funktionenkörper, J. reine angew. Math, vol.173, pp.43-51, 1935.

G. Frey and H. Rück, A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Math. Comp, vol.62, issue.206, pp.865-874, 1994.

R. Granger, F. Hess, R. Oyono, N. Theriault, and F. Vercauteren, Ate Pairing on Hyperelliptic Curves, Advances in Cryptology ? EUROCRYPT 2007, pp.430-447, 2007.
DOI : 10.1007/978-3-540-72540-4_25

F. Hess, Pairing Lattices, Pairing-Based Cryptography ? Pairing, pp.18-38, 2008.
DOI : 10.1007/978-3-540-85538-5_2

F. Hess, N. Smart, and F. Vercauteren, The Eta Pairing Revisited, IEEE Transactions on Information Theory, vol.52, issue.10, pp.4595-4602, 2006.
DOI : 10.1109/TIT.2006.881709

E. W. Howe, The Weil pairing and the Hilbert symbol, Mathematische Annalen, vol.40, issue.1, pp.337-392, 1996.
DOI : 10.1007/BF01444229

S. Lichtenbaum, Duality theorems for curves overP-adic fields, Inventiones Mathematicae, vol.27, issue.2, pp.120-136, 1969.
DOI : 10.1007/BF01389795

J. Tate, WC-groups over p-adic fields, pp.265-277, 1956.

F. Vercauteren, Optimal Pairings, IEEE Transactions on Information Theory, vol.56, issue.1, pp.455-461, 2010.
DOI : 10.1109/TIT.2009.2034881