Bibliography

Major publications by the team in recent years

1A. 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
2J. 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.
3A. 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
4L. De Feo, É. Schost.

Fast Arithmetics in Artin-Schreier towers, in: ISSAC 2009, 2009, p. 121-134.
5A. 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
6A. Enge, P. Gaudry.

A general framework for subexponential discrete logarithm algorithms, in: Acta Arith., 2002, vol. CII, n^o 1, p. 83–103.
7A. Enge, P. Gaudry.

An $L (1 / 3 + ε$ ) 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
8A. Enge, F. Morain.

Comparing Invariants for Class Fields of Imaginary Quadratic Fields, in: Algorithmic Number Theory, C. Fieker, D. 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.
9A. 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
10P. 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
11F. 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.
12F. 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
13F. Morain.

Implementing the asymptotically fast version of the elliptic curve primality proving algorithm, in: Math. Comp., 2007, vol. 76, p. 493–505.
14B. 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.

Publications of the year

Articles in International Peer-Reviewed Journal

15A. Couvreur.

Construction of rational surfaces yielding good codes, in: Finite Fields and Their Applications, September 2011, vol. 17, n^o 5, p. 424-441. [ DOI : 10.1016/j.ffa.2011.02.007 ]

http://hal.inria.fr/inria-00547454/en
16A. Couvreur.

Differential Approach for the Study of Duals of Algebraic-Geometric Codes on Surfaces, in: Journal de Théorie des Nombres de Bordeaux, January 2011, vol. 23, n^o 1, p. 95-120.

http://hal.inria.fr/inria-00541894/en
17A. Couvreur.

Incidence structures from the blown-up plane and LDPC codes, in: IEEE Transactions on Information Theory, July 2011, vol. 57, n^o 7, p. 4401 - 4416, Ce travail a été partiellement financé par l'ANR-08-EMER-003, Projet COCQ. [ DOI : 10.1109/TIT.2011.2146490 ]

http://hal.inria.fr/inria-00540023/en
18L. De Feo.

Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic, in: Journal of Number Theory, May 2011, vol. 131, n^o 5, p. 873-893. [ DOI : 10.1016/j.jnt.2010.07.003 ]

http://hal.inria.fr/hal-00505798/en
19C. Munuera, M. Barbier.

Wet paper codes and the dual distance in steganography, in: Advances in mathematics of communications, November 2011.

http://hal.inria.fr/inria-00584877/en
20B. Smith.

Families of explicitly isogenous Jacobians of variable-separated curves, in: LMS Journal of Computation and Mathematics, August 2011, vol. 14, p. 179-199. [ DOI : 10.1112/S1461157010000410 ]

http://hal.inria.fr/inria-00516038/en
21A. Zeh, C. Gentner, D. Augot.

An Interpolation Procedure for List Decoding Reed–Solomon codes Based on Generalized Key Equations, in: IEEE Transactions on Information Theory, September 2011. [ DOI : 10.1109/TIT.2011.2162160 ]

http://hal.inria.fr/inria-00633205/en

International Conferences with Proceedings

22F. Armknecht, D. Augot, L. Perret, A.-R. Sadeghi.

On constructing homomorphic encryption schemes from coding theory, in: IMA International Conference on Cryptography and Coding, Oxford, Royaume-Uni, L. Chen (editor), Springer, December 2011.

http://hal.inria.fr/hal-00643774/en/
23D. Augot, M. Barbier, A. Couvreur.

List-Decoding of Binary Goppa Codes up to the Binary Johnson Bound, in: IEEE Information Theory Workshop, Paraty, Brésil, S. Amin, V. C. da Rocha Jr., S. I. R. Costa (editors), IEEE, October 2011.

http://hal.inria.fr/hal-00643794/en/
24D. Augot, M. Barbier, C. Fontaine.

Ensuring message embedding in wet paper steganography, in: IMACC 2011, Oxford, United Kingdom, L. Chen (editor), Lecture Notes in Computer Science, November 2011.

http://hal.inria.fr/hal-00639551/en
25M. Barbier, P. S. L. M. Barreto.

Key Reduction of McEliece's Cryptosystem Using List Decoding, in: International Symposium of Information Theory (ISIT), Saint-Peterburg, Russian Federation, A. Kuleshov, V. M. Blinovsky, A. Ephremides (editors), IEEE, August 2011, p. 2657-2661.

http://hal.inria.fr/inria-00565343/en

Scientific Books (or Scientific Book chapters)

27A. Guillevic, N. El Mrabet, S. Ionica.

Efficient multiplication in finite field extensions of degree 5, in: Progress in Cryptology-Africacrypt 2011, Springer, June 2011, n^o 6737, p. 188-205.

http://hal.inria.fr/inria-00609920/en

Internal Reports

28S. Ionica, A. Joux.

Pairing the Volcano, October 2011.

http://hal.inria.fr/hal-00448031/en

Other Publications

29M. Barbier, C. Chabot, G. Quintin.

On Quasi-Cyclic Codes as a Generalization of Cyclic Codes, 2011, under submission.

http://hal.inria.fr/inria-00615276/en
30J. Berthomieu, G. Lecerf, G. Quintin.

Polynomial root finding over local rings and application to error correcting codes, This work has been partly supported by the French ANR-09-JCJC-0098-01 MaGiX project, and by the Digiteo 2009-36HD grant of the Région Île-de-France..

http://hal.inria.fr/hal-00642075/en/
31B. Smith.

Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method.

http://hal.inria.fr/inria-00632118/en

References in notes

32L. 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.
33D. Bernstein.

Proving primality in essentially quartic expected time, in: Math. Comp., 2007, vol. 76, p. 389–403.
34A. 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
35S. Contini.

Factoring integers with the self-initializing quadratic sieve, 1997.

http://www.crypto-world.com/documents/contini_siqs.pdf
36J.-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.
37J.-M. Couveignes.

Quelques calculs en théorie des nombres, Université de Bordeaux I, July 1994.
38J.-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.
39C. 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.
40R. Dupont.

Moyenne arithmético-géométrique, suites de Borchardt et applications, École polytechnique, 2006.
41R. 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://hal.inria.fr/inria-00386299
42A. 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.
43A. 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.
44A. 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.
45J. 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.
46P. 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
47P. 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.
48P. 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.
49P. 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. [ DOI : 10.1145/1145768.1145791 ]

http://hal.inria.fr/inria-00001009
50P. 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
51P. 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
52P. Gaudry, É. Schost.

Genus 2 point counting over prime fields, 2011, To appear in J. Symb. Comput..
53P. 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
54J. E. Gower, S. S. Wagstaff, Jr..

Square form factorization, in: Math. Comp., 2008, vol. 77, p. 551–588.
55V. 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.
56F. Hess.

Computing Relations in Divisor Class Groups of Algebraic Curves over Finite Fields, 2004, Draft version.

http://www.math.tu-berlin.de/~hess/personal/dlog.ps.gz
57T. Høholdt, J. H. van Lint, R. Pellikaan.

Algebraic geometry codes, in: Handbook of Coding Theory, Elsevier, 1998, vol. I, p. 871–961.
58D. 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.
59H. W. Jr. Lenstra, C. Pomerance.

Primality testing with Gaussian periods, July 2005, Preliminary version.

http://www.math.dartmouth.edu/~carlp/PDF/complexity072805.pdf
60R. Lercier.

Computing isogenies in $F_{2^{n}}$ , 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.
61R. Lercier, F. Morain.

Computing isogenies between elliptic curves over $F_{p^{n}}$ using Couveignes's algorithm, in: Math. Comp., January 2000, vol. 69, n^o 229, p. 351–370.
62J. McKee.

Speeding Fermat's Factoring Method, in: Math. Comp., October 1999, vol. 68, n^o 228, p. 1729-1737.
63F. Morain.

Elliptic curves for primality proving, in: Encyclopedia of cryptography and security, H. C. A. van Tilborg (editor), Springer, 2005.
64M. A. Morrison, J. Brillhart.

A method of factoring and the factorization of $F_{7}$ , in: Math. Comp., January 1975, vol. 29, n^o 129, p. 183-205.
65A. Rostovtsev, A. Stolbunov.

Public-key cryptosystem based on isogenies, 2006, Cryptology ePrint Archive, Report 2006/145.

http://eprint.iacr.org/
66A. Sutherland.

Computing Hilbert class polynomials with the CRT method, 2008, Talk at the 12th Workshop on Elliptic Curve Cryptography (ECC).

http://www.hyperelliptic.org/tanja/conf/ECC08/slides/Andrew-V-Sutherland.pdf
67E. Teske.

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

Previous |

Home