Bibliography

Major publications by the team in recent years

[1]

A. Basiri, A. Enge, J.-C. Faugère, N. Gürel.
The Arithmetic of Jacobian Groups of Superelliptic Cubics, in: Math. Comp., 2005, vol. 74, p. 389–410
http://hal.inria.fr/inria-00071967.

[2]

J. Belding, R. Bröker, A. Enge, K. Lauter.
Computing Hilbert class polynomials, in: Algorithmic number theory, Berlin, Lecture Notes in Comput. Sci., Springer, 2008, vol. 5011, p. 282–295.

[3]

A. Bostan, F. Morain, B. Salvy, É. Schost.
Fast algorithms for computing isogenies between elliptic curves, in: Math. Comp., 2008, vol. 77, n^o 263, p. 1755–1778
http://dx.doi.org/10.1090/S0025-5718-08-02066-8.

[4]

A. Enge.
The complexity of class polynomial computation via floating point approximations, in: Mathematics of Computation, 2008, vol. 78, p. 1089-1107
http://hal.inria.fr/inria-00001040/PDF/class.pdf.

[5]

A. Enge, P. Gaudry.
A general framework for subexponential discrete logarithm algorithms, in: Acta Arith., 2002, vol. CII, n^o 1, p. 83–103.

[6]

A. Enge, P. Gaudry.
An L(1/3 + ) algorithm for the discrete logarithm problem for low degree curves, in: Advances in Cryptology — Eurocrypt 2007, Berlin, M. Naor (editor), Lecture Notes in Comput. Sci., Springer-Verlag, 2007, vol. 4515, p. 379–393
http://hal.inria.fr/inria-00135324.

[7]

A. Enge, F. Morain.
Comparing Invariants for Class Fields of Imaginary Quadratic Fields, in: Algorithmic Number Theory, C. Fieker, D. R. Kohel (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 2002, vol. 2369, p. 252–266, 5th International Symposium, ANTS-V, Sydney, Australia, July 2002, Proceedings.

[8]

A. Enge, R. Schertz.
Constructing elliptic curves over finite fields using double eta-quotients, in: Journal de Théorie des Nombres de Bordeaux, 2004, vol. 16, p. 555–568
http://jtnb.cedram.org/jtnb-bin/fitem?id=JTNB_2004__16_3_555_0.

[9]

P. Mihăilescu, F. Morain, É. Schost.
Computing the eigenvalue in the Schoof-Elkies-Atkin algorithm using Abelian lifts, in: ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation, New York, NY, USA, ACM Press, 2007, p. 285–292
http://hal.inria.fr/inria-00130142.

[10]

F. Morain.
La primalité en temps polynomial [d'après Adleman, Huang; Agrawal, Kayal, Saxena], in: Astérisque, 2004, n^o 294, p. Exp. No. 917, 205–230, Séminaire Bourbaki. Vol. 2002/2003.

[11]

F. Morain.
Computing the cardinality of CM elliptic curves using torsion points, in: Journal de Théorie des Nombres de Bordeaux, 2007, vol. 19, n^o 3, p. 663–681
http://arxiv.org/ps/math.NT/0210173.

[12]

F. Morain.
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm, in: Math. Comp., 2007, vol. 76, p. 493–505.

Publications of the year

Articles in International Peer-Reviewed Journal

[13]

D. Augot, C. Gentner, A. Zeh.
A Berlekamp-Massey Approach for the Guruswami-Sudan Decoding Algorithm for Reed-Solomon Codes, in: IEEE Transactions on Information Theory, submitted 2009.

[14]

R. Dupont.
Fast evaluation of modular functions using Newton iterations and the AGM, in: Math. Comp., 2009
http://www.lix.polytechnique.fr/Labo/Regis.Dupont/preprints/Dupont_FastEvalMod.ps.gz, To appear.

[15]

A. Enge.
Computing modular polynomials in quasi-linear time, in: Math. Comp., 2009, vol. 78, p. 1809-1024
http://hal.inria.fr/inria-00143084/PDF/modcomp.pdf.

[16]

S. Galbraith, J. Pujolas, C. Ritzenthaler, B. Smith.
Distortion Maps for Genus 2 Curves, in: Journal of Mathematical Cryptology, 2009.

[17]

B. Smith.
Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves, in: J. of Cryptology, 2009, vol. 22, n^o 4, p. 505-529.

International Peer-Reviewed Conference/Proceedings

[18]

F. Armknecht, D. Augot, L. Perret, A.-R. Sadeghi.
Algebraically Homomorphic Encryption from Evaluation Codes, in: EUROCRYPT 2010, 2009, submitted.

[19]

L. De Feo, É. Schost.
Fast Arithmetics in Artin-Schreier towers, in: ISSAC 2009, 2009, p. 121-134.

[20]

B. Smith.
Families of explicit isogenies of hyperelliptic Jacobians, in: Arithmétique, géométrie, cryptographie et théorie des codes: AGCT 12, 2009, submitted.

Other Publications

[21]

A. Enge, F. Morain.
Generalised Weber Functions. I, 2009
http://hal.inria.fr/inria-00385608/en/.

[22]

The CADO Team.
CADO — Number field sieve: distribution, optimization, 2009
http://cado.gforge.inria.fr/.

References in notes

[23]

L. M. Adleman, J. DeMarrais, M.-D. Huang.
A Subexponential Algorithm for Discrete Logarithms over the Rational Subgroup of the Jacobians of Large Genus Hyperelliptic Curves over Finite Fields, in: Algorithmic Number Theory, Berlin, L. M. Adleman, M.-D. Huang (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 1994, vol. 877, p. 28–40.

[24]

P. S. L. M. Barreto, B. Lynn, M. Scott.
Constructing Elliptic Curves with Prescribed Embedding Degrees, in: Security in Communication Networks — Third International Conference, SCN 2002, Amalfi, Italy, September 2002, Berlin, S. Cimato, C. Galdi, G. Persiano (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 2003, vol. 2576, p. 257–267.

[25]

D. Bernstein.
Proving primality in essentially quartic expected time, in: Math. Comp., 2007, vol. 76, p. 389–403.

[26]

A. Bostan, P. Gaudry, É. Schost.
Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves, in: Finite Fields and Applications, 7th International Conference, Fq7, G. Mullen, A. Poli, H. Stichtenoth (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 2004, vol. 2948, p. 40–58
http://www.lix.polytechnique.fr/Labo/Pierrick.Gaudry/publis/cartierFq7.ps.gz.

[27]

S. Contini.
Factoring integers with the self-initializing quadratic sieve, 1997
http://citeseer.ist.psu.edu/contini97factoring.html.

[28]

J.-M. Couveignes.
Algebraic Groups and Discrete Logarithm, in: Public-Key Cryptography and Computational Number Theory, Berlin, K. Alster, J. Urbanowicz, H. C. Williams (editors), De Gruyter, 2001, p. 17–27.

[29]

J.-M. Couveignes.
Quelques calculs en théorie des nombres, Université de Bordeaux I, July 1994, Thèse.

[30]

J.-M. Couveignes.
Computing l -isogenies using the p -torsion, in: Algorithmic Number Theory, H. Cohen (editor), Lecture Notes in Comput. Sci., Springer Verlag, 1996, vol. 1122, p. 59–65, Second International Symposium, ANTS-II, Talence, France, May 1996, Proceedings.

[31]

C. Diem.
An Index Calculus Algorithm for Plane Curves of Small Degree, in: Algorithmic Number Theory — ANTS-VII, Berlin, F. Hess, S. Pauli, M. Pohst (editors), Lecture Notes in Computer Science, Springer-Verlag, 2006, vol. 4076, p. 543–557.

[32]

R. Dupont.
Moyenne arithmético-géométrique, suites de Borchardt et applications, École polytechnique, 2006, Ph. D. Thesis.

[33]

R. Dupont, A. Enge, F. Morain.
Building curves with arbitrary small MOV degree over finite prime fields, in: J. of Cryptology, 2005, vol. 18, n^o 2, p. 79–89
http://www.math.u-bordeaux1.fr/~enge/vorabdrucke/mov.ps.gz.

[34]

A. Enge.
A General Framework for Subexponential Discrete Logarithm Algorithms in Groups of Unknown Order, in: Finite Geometries, Dordrecht, A. Blokhuis, J. W. P. Hirschfeld, D. Jungnickel, J. A. Thas (editors), Developments in Mathematics, Kluwer Academic Publishers, 2001, vol. 3, p. 133–146.

[35]

A. Enge.
Computing Discrete Logarithms in High-Genus Hyperelliptic Jacobians in Provably Subexponential Time, in: Math. Comp., 2002, vol. 71, n^o 238, p. 729–742.

[36]

A. Enge, F. Morain.
Fast decomposition of polynomials with known Galois group, in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, M. Fossorier, T. Høholdt, A. Poli (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 2003, vol. 2643, p. 254–264, 15th International Symposium, AAECC-15, Toulouse, France, May 2003, Proceedings.

[37]

C. Fontaine, F. Galand.
How Can Reed-Solomon Codes Improve Steganographic Schemes?, in: Information Hiding, T. Furon, F. Cayre, G. Doërr, P. Bas (editors), Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 2007, n^o 4567, p. 130–144.

[38]

J. Franke, T. Kleinjung, F. Morain, T. Wirth.
Proving the primality of very large numbers with fastECPP, in: Algorithmic Number Theory, D. Buell (editor), Lecture Notes in Comput. Sci., Springer-Verlag, 2004, vol. 3076, p. 194–207, 6th International Symposium, ANTS-VI, Burlington, VT, USA, June 2004, Proceedings.

[39]

P. Gaudry, N. Gürel.
Counting points in medium characteristic using Kedlaya's algorithm, in: Experiment. Math., 2003, vol. 12, n^o 4, p. 395–402
http://www.expmath.org/expmath/volumes/12/12.html.

[40]

P. Gaudry.
An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves, in: Advances in Cryptology — EUROCRYPT 2000, Berlin, B. Preneel (editor), Lecture Notes in Comput. Sci., Springer-Verlag, 2000, vol. 1807, p. 19–34.

[41]

P. Gaudry.
A comparison and a combination of SST and AGM algorithms for counting points of elliptic curves in characteristic 2, in: Advances in Cryptology – ASIACRYPT 2002, Y. Zheng (editor), Lecture Notes in Comput. Sci., Springer–Verlag, 2002, vol. 2501, p. 311–327.

[42]

P. Gaudry, F. Morain.
Fast algorithms for computing the eigenvalue in the Schoof-Elkies-Atkin algorithm, in: ISSAC '06: Proceedings of the 2006 international symposium on Symbolic and algebraic computation, New York, NY, USA, ACM Press, 2006, p. 109–115
http://hal.inria.fr/inria-00001009.

[43]

P. Gaudry, É. Schost.
Construction of Secure Random Curves of Genus 2 over Prime Fields, in: Advances in Cryptology – EUROCRYPT 2004, C. Cachin, J. Camenisch (editors), Lecture Notes in Comput. Sci., Springer-Verlag, 2004, vol. 3027, p. 239–256
http://www.lix.polytechnique.fr/Labo/Pierrick.Gaudry/publis/secureg2.ps.gz.

[44]

P. Gaudry, É. Schost.
Modular equations for hyperelliptic curves, in: Math. Comp., 2005, vol. 74, p. 429–454
http://www.lix.polytechnique.fr/Labo/Pierrick.Gaudry/publis/eqmod2.ps.gz.

[45]

P. Gaudry, E. Thomé, N. Thériault, C. Diem.
A double large prime variation for small genus hyperelliptic index calculus, in: Math. Comp., 2007, vol. 76, p. 475–492
http://www.loria.fr/~gaudry/publis/dbleLP.ps.gz.

[46]

C. Gentry.
On Homomorphic Encryption over Circuits of Arbitrary Depth, in: 41st ACM Symposium on Theory of Computing (STOC 2009), 2009.

[47]

J. E. Gower, S. S. Wagstaff, Jr..
Square form factorization, in: Math. Comp., 2008, vol. 77, p. 551–588.

[48]

V. Guruswami, M. Sudan.
Improved decoding of Reed-Solomon and algebraic-geometry codes, in: IEEE Transactions on Information Theory, 1999, vol. 45, n^o 6, p. 1757–1767.

[49]

F. Hess.
Computing Relations in Divisor Class Groups of Algebraic Curves over Finite Fields, 2004
http://www.math.tu-berlin.de/~hess/personal/dlog.ps.gz, Draft version.

[50]

T. Høholdt, J. H. van Lint, R. Pellikaan.
Algebraic geometry codes, in: Handbook of Coding Theory, Elsevier, 1998, vol. I, p. 871–961.

[51]

M. Jacobson.
Subexponential Class Group Computation in Quadratic Orders, Technische Universität Darmstadt, Darmstadt, Germany, 1999, Ph. D. Thesis.

[52]

D. Jao, S. D. Miller, R. Venkatesan.
Do All Elliptic Curves of the Same Order Have the Same Difficulty of Discrete Log?, in: ASIACRYPT, Lecture Notes in Comput. Sci., 2005, p. 21-40.

[53]

A. Joux.
A One Round Protocol for Tripartite Diffie–Hellman, in: Algorithmic Number Theory — ANTS-IV, Berlin, W. Bosma (editor), Lecture Notes in Comput. Sci., Springer-Verlag, 2000, vol. 1838, p. 385–393.

[54]

H. W. Jr. Lenstra, C. Pomerance.
Primality testing with Gaussian periods, July 2005
http://www.math.dartmouth.edu/~carlp/PDF/complexity072805.pdf, Preliminary version.

[55]

R. Lercier.
Computing isogenies in F_2ⁿ , in: Algorithmic Number Theory, H. Cohen (editor), Lecture Notes in Comput. Sci., Springer Verlag, 1996, vol. 1122, p. 197–212, Second International Symposium, ANTS-II, Talence, France, May 1996, Proceedings.

[56]

R. Lercier, F. Morain.
Computing isogenies between elliptic curves over F_pⁿ using Couveignes's algorithm, in: Math. Comp., January 2000, vol. 69, n^o 229, p. 351–370.

[57]

J. McKee.
Speeding Fermat's Factoring Method, in: Math. Comp., October 1999, vol. 68, n^o 228, p. 1729-1737.

[58]

F. Morain.
Elliptic curves for primality proving, in: Encyclopedia of cryptography and security, H. C. A. van Tilborg (editor), Springer, 2005.

[59]

M. A. Morrison, J. Brillhart.
A method of factoring and the factorization of F₇ , in: Math. Comp., January 1975, vol. 29, n^o 129, p. 183-205.

[60]

A. Rostovtsev, A. Stolbunov.
Public-key cryptosystem based on isogenies, 2006
http://eprint.iacr.org/, Cryptology ePrint Archive, Report 2006/145.

[61]

R. Sakai, K. Ohgishi, M. Kasahara.
Cryptosystems based on pairing, 2000, SCIS 2000, The 2000 Symposium on Cryptography and Information Security, Okinawa, Japan, January 26–28.

[62]

A. Sutherland.
Computing Hilbert class polynomials with the CRT method, 2008
http://www.hyperelliptic.org/tanja/conf/ECC08/slides/Andrew-V-Sutherland.pdf, Talk at the 12th Workshop on Elliptic Curve Cryptography (ECC).

[63]

E. Teske.
An elliptic trapdoor system, in: J. of Cryptology, 2006, vol. 19, n^o 1, p. 115–133.

[64]

Y. Wu.
New List Decoding Algorithms for Reed-Solomon and BCH Codes, in: Information Theory, IEEE Transactions on, 2008, vol. 54, n^o 8, p. 3611–3630
http://dx.doi.org/10.1109/TIT.2008.926355.