| [1] |
Bill Allombert.
An efficient algorithm for the computation of Galois automorphisms.
Math. Comp., 73(245):359–375 (electronic), 2004. |
| [2] |
David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor, and Eric W. Weisstein.
Ten problems in experimental mathematics.
Amer. Math. Monthly, 113(6):481–509, 2006. |
| [3] |
Stéphane Ballet.
Quasi-optimal algorithms for multiplication in the extensions of
F16 of degree 13, 14 and 15.
J. Pure Appl. Algebra, 171(2-3):149–164, 2002. |
| [4] |
Peter Birkner.
Efficient divisor class halving on genus two curves.
Preprint, 10 pages, 2006. |
| [5] |
Werner Bley and Robert Boltje.
Computation of locally free class groups.
In Algorithmic Number Theory, volume 4076 of Lecture
Notes in Comput. Sci., pages 72–86. Springer, Berlin, 2006. |
| [6] |
Jonathan Borwein and David Bailey.
Mathematics by Experiment.
A K Peters Ltd., Natick, MA, 2004. |
| [7] |
Wieb Bosma.
Some computational experiments in number theory.
In Discovering Mathematics with Magma, volume 19 of Algorithms Comput. Math., pages 1–30. Springer, Berlin, 2006. |
| [8] |
Wieb Bosma, John Cannon, and Allan Steel.
Lattices of compatibly embedded finite fields.
J. Symbolic Comput., 24(3-4):351–369, 1997. |
| [9] |
Wieb Bosma and Bart de Smit.
Class number relations from a computational point of view.
J. Symbolic Comput., 31(1-2):97–112, 2001. |
| [10] |
Wieb Bosma and Bart de Smit.
On arithmetically equivalent number fields of small degree.
In Algorithmic Number Theory (Sydney, 2002), volume 2369 of
Lecture Notes in Comput. Sci., pages 67–79. Springer, Berlin, 2002. |
| [11] |
Wieb Bosma and Arjen K. Lenstra.
An implementation of the elliptic curve integer factorization method.
In Computational Algebra and Number Theory (Sydney,
1992), volume 325 of Math. Appl., pages 119–136. Kluwer Acad. Publ.,
Dordrecht, 1995. |
| [12] |
Wieb Bosma and Peter Stevenhagen.
Density computations for real quadratic units.
Math. Comp., 65(215):1327–1337, 1996. |
| [13] |
Johan Bosman.
A polynomial with Galois group SL2(F16).
arXiv:math/0701442, 7 pages, 2007. |
| [14] |
Alin Bostan, Pierrick Gaudry, and Éric Schost.
Linear recurrences with polynomial coefficients and computation of
the Cartier-Manin operator on hyperelliptic curves.
In Finite Fields and Applications, volume 2948 of Lecture Notes in Comput. Sci., pages 40–58. Springer, Berlin, 2004. |
| [15] |
Richard P. Brent.
Factorization of the tenth Fermat number.
Math. Comp., 68(225):429–451, 1999. |
| [16] |
Richard P. Brent.
Recent progress and prospects for integer factorisation algorithms.
In Computing and Combinatorics (Sydney, 2000), volume 1858 of
Lecture Notes in Comput. Sci., pages 3–22. Springer, Berlin, 2000. |
| [17] |
Richard P. Brent.
Note on Marsaglia's xorshift random number generators.
J. Stat. Soft, 11(5):1–5, 2004. |
| [18] |
Nils Bruin and Michael Stoll.
Deciding existence of rational points on curves: an experiment.
arXiv:math.NT/0604524, 12 pages, 2006. |
| [19] |
David G. Cantor and Daniel M. Gordon.
Factoring polynomials over p-adic fields.
In Algorithmic Number Theory (Leiden, 2000), volume 1838 of
Lecture Notes in Comput. Sci., pages 185–208. Springer, Berlin, 2000. |
| [20] |
R. Carls, D. Kohel, and D. Lubicz.
Higher dimensional 3-adic CM construction.
arXiv:math/0607583, 14 pages, 2006. |
| [21] |
Antoine Chambert-Loir.
Compter (rapidement) le nombre de solutions d'equations dans les
corps finis.
arXiv:math.NT/0611584, 46 pages, 2006. |
| [22] |
J. E. Cremona and D. Rusin.
Efficient solution of rational conics.
Math. Comp., 72(243):1417–1441 (electronic), 2003. |
| [23] |
M. Daberkow.
Computing with subfields.
J. Symbolic Comput., 24(3-4):371–384, 1997. |
| [24] |
M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner, M. Schörnig,
and K. Wildanger.
KANT V4.
J. Symbolic Comput., 24(3-4):267–283, 1997. |
| [25] |
Lassina Dembélé.
Quaternionic Manin symbols, Brandt matrices, and Hilbert
modular forms.
Math. Comp., 76(258):1039–1057 (electronic), 2007. |
| [26] |
Francisco Diaz y Diaz, Jean-François Jaulent, Sebastian Pauli, Michael
Pohst, and Florence Soriano-Gafiuk.
A new algorithm for the computation of logarithmic l-class groups
of number fields.
Experiment. Math., 14(1):65–74, 2005. |
| [27] |
Claus Diem.
Index calculus in class groups of plane curves of small degree.
Preprint, 43 pages, 2005. |
| [28] |
Claus Diem.
An index calculus algorithm for plane curves of small degree.
In Algorithmic Number Theory, volume 4076 of Lecture
Notes in Comput. Sci., pages 543–557. Springer, Berlin, 2006. |
| [29] |
Jintai Ding, Jason E. Gower, and Dieter S. Schmidt.
Zhuang-Zi: A new algorithm for solving multivariate polynomial
equations over a finite field.
Preprint, 14 pages, 2006. |
| [30] |
Jacques Dubrois and Jean-Guillaume Dumas.
Efficient polynomial time algorithms computing industrial-strength
primitive roots.
Inform. Process. Lett., 97(2):41–45, 2006. |
| [31] |
I. Duursma, P. Gaudry, and F. Morain.
Speeding up the discrete log computation on curves with
automorphisms.
In Advances in Cryptology—Asiacrypt'99 (Singapore), volume
1716 of Lecture Notes in Comput. Sci., pages 103–121. Springer,
Berlin, 1999. |
| [32] |
Claus Fieker.
Applications of the class field theory of global fields.
In Discovering Mathematics with Magma, volume 19 of Algorithms Comput. Math., pages 31–62. Springer, Berlin, 2006. |
| [33] |
Claus Fieker.
Sparse representation for cyclotomic fields.
Preprint, 12 pages, 2006. |
| [34] |
Claus Fieker and Willem A. de Graaf.
Finding integeral linear dependencies of algebraic numbers and
algebraic Lie algebars.
LMS J. Comput. Math., 10:271–287, 2007. |
| [35] |
Claus Fieker and Michael E. Pohst.
Dependency of units in number fields.
Math. Comp., 75(255):1507–1518 (electronic), 2006. |
| [36] |
Tom Fisher.
The Hessian of a genus one curve.
arXiv:math.NT/0610403, 28 pages, 2006. |
| [37] |
Tom Fisher.
The invariants of a genus one curve.
arXiv:math.NT/0610318, 37 pages, 2006. |
| [38] |
Robert Fraatz.
Computation of Maximal Orders of Cyclic Extensions of Function
Fields.
PhD Thesis, Technischen Universtät Berlin, 2005. |
| [39] |
P. Gaudry, T. Houtmann, D. Kohel, C. Ritzenthaler, and A. Weng.
The p-adic CM-method for genus 2.
arXiv:math.NT/0503148 v1, 24 pages, 2005. |
| [40] |
Pierrick Gaudry.
An algorithm for solving the discrete log problem on hyperelliptic
curves.
In Advances in Cryptology—Eurocrypt 2000 (Bruges), volume
1807 of Lecture Notes in Comput. Sci., pages 19–34. Springer, Berlin,
2000. |
| [41] |
Willi Geiselmann, Jörn Müller-Quade, and Rainer Steinwandt.
Comment on: ``A new representation of elements of finite fields
GF(2m) yielding small complexity arithmetic circuits'' by G.
Drolet.
IEEE Trans. Comput., 51(12):1460–1461, 2002. |
| [42] |
Willi Geiselmann and Rainer Steinwandt.
A redundant representation of GF(qn) for designing
arithmetic circuits.
IEEE Trans Comp, 52(7):848–853, 2003. |
| [43] |
Willi Geiselmann and Rainer Steinwandt.
Non-wafer-scale sieving hardware for the NFS: Another attempt to
cope with 1024-bit.
Preprint, page 13, 2006. |
| [44] |
Martine Girard and Leopoldo Kulesz.
Computation of sets of rational points of genus-3 curves via the
Demjanenko-Manin method.
LMS J. Comput. Math., 8:267–300 (electronic), 2005. |
| [45] |
Norbert Goeb.
Computing the automorphism groups of hyperelliptic function fields.
arXiv:math.NT/0305284, 16 pages, 2003. |
| [46] |
G. Hanrot and F. Morain.
Solvability by radicals from an algorithmic point of view.
In Proceedings of the 2001 International Symposium on Symbolic
and Algebraic Computation, pages 175–182 (electronic), New York, 2001. ACM. |
| [47] |
Lenwood S. Heath and Nicholas A. Loehr.
New algorithms for generating Conway polynomials over finite
fields.
In SODA '99: Proceedings of the tenth annual ACM-SIAM symposium
on Discrete algorithms, pages 429–437, Philadelphia, PA, USA, 1999. Society
for Industrial and Applied Mathematics. |
| [48] |
Lenwood S. Heath and Nicholas A. Loehr.
New algorithms for generating Conway polynomials over finite
fields.
J. Symbolic Comput., 38(2):1003–1024, 2004. |
| [49] |
Florian Hess, Sebastian Pauli, and Michael E. Pohst.
Computing the multiplicative group of residue class rings.
Math. Comp., 72(243):1531–1548 (electronic), 2003. |
| [50] |
Hendrik Hubrechts.
Quasi-quadratic elliptic curve point counting using rigid cohomology.
arXiv:math/0701850, 14 pages, 2007. |
| [51] |
Antoine Joux and Reynald Lercier.
Counting points on elliptic curves in medium characteristic.
Preprint, page 15, 2006. |
| [52] |
Jürgen Klüners.
Algorithms for function fields.
Experiment. Math., 11(2):171–181, 2002. |
| [53] |
Siguna Müller.
On the computation of square roots in finite fields.
Des. Codes Cryptogr., 31(3):301–312, 2004. |
| [54] |
Titus Piezas.
Solving solvable sextics using polynomial decomposition.
Preprint, 22 pages, 2004. |
| [55] |
Xavier-François Roblot.
Polynomial factorization algorithms over number fields.
J. Symbolic Comput., 38(5):1429–1443, 2004. |
| [56] |
Nigel P. Smart.
The Algorithmic Resolution of Diophantine Equations,
volume 41 of London Mathematical Society Student Texts.
Cambridge University Press, Cambridge, 1998. |
| [57] |
Damien Stehlé and Paul Zimmermann.
A binary recursive GCD algorithm.
In Algorithmic Number Theory, volume 3076 of Lecture
Notes in Comput. Sci., pages 411–425. Springer, Berlin, 2004. |
| [58] |
Katsuyuki Takashima.
A new type of fast endomorphisms on Jacobians of hyperelliptic
curves and their cryptographic application.
IEICE Trans. Fundamentals, E89-A(1):124–133, 2006. |
| [59] |
Mark van Hoeij.
Factoring polynomials and the knapsack problem.
J. Number Theory, 95(2):167–189, 2002. |
| [60] |
Paul Zimmermann and Bruce Dodson.
20 years of ECM.
In Algorithmic Number Theory, volume 4076 of Lecture
Notes in Comput. Sci., pages 525–542. Springer, Berlin, 2006. |
