A. Bostan, F. Morain, B. Salvy, and . Schost, Fast algorithms for computing isogenies between elliptic curves, Mathematics of Computation, vol.77, issue.263, pp.1755-1778, 2008.

Q. Cheng, Straight-line programs and torsion points on elliptic curves, computational complexity, vol.12, issue.3-4, pp.150-161, 2003.

C. Costello, H. Hisil, and B. Smith, Faster Compact Diffie???Hellman: Endomorphisms on the x-line, Advances in Cryptology -EUROCRYPT 2014 -33rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp.183-200, 2014.

C. Costello and P. Longa, Four $$\mathbb {Q}$$ : Four-Dimensional Decompositions on a $$\mathbb {Q}$$ -curve over the Mersenne Prime, Advances in Cryptology -ASIACRYPT 2015 - 21st International Conference on the Theory and Application of Cryptology and Information Security Proceedings, Part I, pp.214-235, 2015.

J. Couveignes and F. Morain, Schoof's algorithm and isogeny cycles, Algorithmic Number Theory 1st Algorithmic Number Theory Symposium -Cornell University, pp.43-58, 1994.

M. Fouquet and F. Morain, Isogeny Volcanoes and the SEA Algorithm, Algorithmic Number Theory, pp.276-291

J. Von, Z. Gathen, and J. Gerhard, Modern Computer Algebra, 1999.

P. Gaudry and F. Morain, Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm, Proceedings of the 2006 international symposium on Symbolic and algebraic computation , ISSAC '06, pp.109-115, 2006.

J. González, Isogenies of polyquadratic $\mathbb{Q}$-curves to their Galois conjugates, Archiv der Mathematik, vol.77, issue.5, pp.383-390, 2001.
DOI : 10.1007/PL00000508

A. Guillevic and S. Ionica, Four-Dimensional GLV via the Weil Restriction, Sako and Sarkar, pp.79-96

Y. Hasegawa, Q-curves over quadratic fields, Manuscripta Mathematica, vol.141, issue.1, pp.347-364, 1997.
DOI : 10.1007/BF02677859

A. Joux and R. Lercier, Chinese & Match'', an alternative to Atkin's Match and Sort'' method used in the SEA algorithm, Mathematics of Computation, vol.70, issue.234, pp.827-836, 2001.

E. Kaltofen and V. Shoup, Subquadratic-time factoring of polynomials over finite fields, Mathematics of Computation, vol.67, issue.223, pp.1179-1197, 1998.

R. Lercier, Finding Good Random Elliptic Curves for Cryptosystems Defined over $$\mathbb{F}_{{\text{2}}^n }$$, Advances in Cryptology ? EUROCRYPT '97, pp.379-392, 1997.

P. Mih?-ailescu, F. Morain, and . Schost, Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts, ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation, pp.285-292, 2007.

T. Satoh, On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields, Algorithmic Number Theory, 5th International Symposium, ANTS-V Proceedings, volume 2369 of Lecture Notes in Comput. Sci, pp.43-66, 2002.

R. Schoof, Elliptic curves over finite fields and the computation of square roots mod p, Math. Comp, vol.44, pp.483-494, 1985.

R. Schoof, Nonsingular plane cubic curves over finite fields, Journal of Combinatorial Theory, Series A, vol.46, issue.2, pp.183-211, 1987.

R. Schoof, Counting points on elliptic curves over finite fields, Journal de Th??orie des Nombres de Bordeaux, vol.7, issue.1, pp.219-254, 1995.
DOI : 10.5802/jtnb.142

E. Igor, A. V. Shparlinski, and . Sutherland, On the distribution of Atkin and Elkies primes, Found. Comput. Math, vol.14, issue.2, pp.285-297, 2014.

E. Igor, A. V. Shparlinski, and . Sutherland, On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average, LMS J. Comput. Math, vol.18, issue.1, pp.308-322

B. Smith, Families of fast elliptic curves from Q-curves, Sako and Sarkar, pp.61-78

B. Smith, The $$\mathbb {Q}$$ Q -curve Construction for Endomorphism-Accelerated Elliptic Curves, Journal of Cryptology, vol.29, issue.4, 2015.

V. Andrew and . Sutherland, Identifying supersingular elliptic curves, LMS J. Comput. Math, vol.15, pp.317-325, 2012.

V. Andrew and . Sutherland, On the evaluation of modular polynomials, ANTS X?Proceedings of the Tenth Algorithmic Number Theory Symposium, pp.531-555, 2013.