C. Arène, T. Lange, M. Naehrig, and C. Ritzenthaler, Faster computation of the Tate pairing, Journal of Number Theory, vol.131, issue.5, 2009.
DOI : 10.1016/j.jnt.2010.05.013

A. O. Atkin and F. Morain, Elliptic curves and primality proving, Mathematics of Computation, vol.61, issue.203, pp.29-68, 1993.
DOI : 10.1090/S0025-5718-1993-1199989-X
URL : https://hal.archives-ouvertes.fr/inria-00075302

P. S. Barreto, B. Lynn, and M. Scott, Efficient implementation of pairingbased cryptosystems, J. Cryptology, vol.17, issue.4, pp.321-334, 2004.

P. S. Barreto, B. Lynn, and M. Scott, On the Selection of Pairing-Friendly Groups, Selected Areas in Cryptography, pp.17-25, 2004.
DOI : 10.1007/978-3-540-24654-1_2

D. J. Bernstein, P. Birkner, M. Joye, T. Lange, C. D. Peters et al., Twisted Edwards Curves, Progress in Cryptology ? AFRICACRYPT, pp.389-405, 2008.
DOI : 10.1007/978-3-540-68164-9_26

D. J. Bernstein and T. Lange, Faster Addition and Doubling on Elliptic Curves, Advances in Cryptology ? ASIACRYPT 2007, pp.29-50, 2007.
DOI : 10.1007/978-3-540-76900-2_3
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.4261

D. J. Bernstein and T. Lange, Inverted Edwards Coordinates, Lect. Notes Comput. Sci, vol.4851, pp.20-27, 2007.
DOI : 10.1007/978-3-540-77224-8_4
URL : http://repository.tue.nl/664250

D. J. Bernstein, T. Lange, and R. R. Farashahi, Binary Edwards Curves, Cryptographic Hardware and Embedded Systems ? CHES 2008, pp.244-265, 2008.
DOI : 10.1007/978-3-540-85053-3_16

I. F. Blake, G. Seroussi, and N. P. Smart, Advances in Elliptic Curve Cryptography, 2005.
DOI : 10.1017/CBO9780511546570

M. P. Das and P. Sarkar, Pairing Computation on Twisted Edwards Form Elliptic Curves, Pairing-Based Cryptography ? Pairing, pp.192-210, 2008.
DOI : 10.1007/978-3-540-85538-5_14

H. M. Edwards, A normal form for elliptic curves, Bulletin of the American Mathematical Society, vol.44, issue.03, pp.393-422, 2007.
DOI : 10.1090/S0273-0979-07-01153-6

S. Goldwasser and J. Kilian, Primality testing using elliptic curves, Journal of the ACM, vol.46, issue.4, pp.450-472, 1999.
DOI : 10.1145/320211.320213

H. Hisil, K. K. Wong, G. Carter, and E. Dawson, Twisted Edwards Curves Revisited, Advances in Cryptology ? ASIACRYPT 2008, pp.326-343, 2008.
DOI : 10.1007/BFb0053453
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.215.3196

G. B. Huff, Diophantine problems in geometry and elliptic ternary forms, Duke Mathematical Journal, vol.15, issue.2, pp.443-453, 1948.
DOI : 10.1215/S0012-7094-48-01543-9

S. Ionica and A. Joux, Another Approach to Pairing Computation in Edwards Coordinates, Progress in Cryptology ? INDOCRYPT 2008, pp.400-413, 2008.
DOI : 10.1007/s00145-004-0315-8

A. H. Koblitz, N. Koblitz, and A. Menezes, Elliptic curve cryptography: The serpentine course of a paradigm shift, Journal of Number Theory, vol.131, issue.5
DOI : 10.1016/j.jnt.2009.01.006

N. Koblitz, Elliptic curve cryptosystems, Mathematics of Computation, vol.48, issue.177, pp.203-209, 1987.
DOI : 10.1090/S0025-5718-1987-0866109-5

H. W. Lenstra and J. , Factoring Integers with Elliptic Curves, The Annals of Mathematics, vol.126, issue.3, pp.649-673, 1987.
DOI : 10.2307/1971363
URL : https://openaccess.leidenuniv.nl/bitstream/handle/1887/2140/346_079.pdf?sequence=1

V. S. Miller, Use of Elliptic Curves in Cryptography, Lect. Notes Comput. Sci, vol.218, pp.417-426, 1986.
DOI : 10.1007/3-540-39799-X_31

V. S. Miller, The Weil paring, and its efficient implementation, J. Cryptology, vol.17, issue.1, pp.235-261, 2004.

P. L. Montgomery, Speeding the Pollard and elliptic curve methods of factorization, Mathematics of Computation, vol.48, issue.177, pp.243-264, 1987.
DOI : 10.1090/S0025-5718-1987-0866113-7

F. Morain, Primality proving using elliptic curves: An update, Algorithmic Number Theory (ANTS-III), pp.111-127, 1998.
DOI : 10.1007/BFb0054855
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.8171

W. D. Peeples and J. , Elliptic curves and rational distance sets, Proc. Am, pp.29-33, 1954.
DOI : 10.1090/S0002-9939-1954-0060262-1

J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, vol.106, 1986.