Papers
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[LRS15]
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R. Lercier, C. Ritzenthaler, and
J. Sijsling. Explicit galois obstruction and descent for
hyperelliptic curves with tamely cyclic reduced automorphism group.
Mathematics of Computation, January 2015.
To appear.
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[CL14]
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J.-M. Couveignes and R. Lercier. The geometry of
some parameterizations and encodings.
Advances in Mathematics of Communications, 8(4):437-458, 2014.
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[EL13]
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T. Ezome and R. Lercier. Elliptic periods and
primality proving.
Journal of Number Theory, 133(1):343-368, 2013.
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[LR12]
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R. Lercier and C. Ritzenthaler. Hyperelliptic
curves and their invariants: geometric, arithmetic and algorithmic aspects.
Journal of Algebra, 372(0):595-636, December 2012.
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[CEL12]
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J.-M. Couveignes, T. Ezome, and R. Lercier. A
faster pseudo-primality test.
Rendiconti del Circolo Matematico di Palermo Journal, 61:261-278,
August 2012.
Springer.
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[CL12]
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J.-M. Couveignes and R. Lercier. Fast construction
of irreducible polynomials over finite fields.
Israel Journal of Mathematics, pages 1-29, May 2012.
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[CEL09]
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J.-M. Couveignes, T. Ezome, and
R. Lercier. Elliptic periods and primality proving (extented
version).
Eprint arXiv:0810.2853v4, June 2009.
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[CL09]
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J.-M. Couveignes and R. Lercier. Elliptic periods
for finite fields.
Finite Fields and their Applications, 15(1):1-22, January 2009.
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[LS08]
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R. Lercier and T. Sirvent. On elkies subgroups of
l-torsion points in elliptic curves defined over a finite field.
Journal de Théorie des Nombres de Bordeaux,
20(3):783-797, December 2008.
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[CL08]
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J.-M. Couveignes and R. Lercier. Galois invariant
smoothness basis.
Series on Number Theory and Its Applications, 5:142-167, May
2008.
World Scientific.
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[LL06]
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R. Lercier and D. Lubicz. A Quasi Quadratic Time
Algorithm for Hyperelliptic Curve Point Counting.
The Ramanujan Journal, 12(3):399-423, December 2006.
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[JL03]
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A. Joux and R. Lercier. Improvements to the
general number field sieve for discrete logarithms in prime fields. A
comparison with the Gaussian integer method.
Mathematics of Computation, 72(242):953-967, April 2003.
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[JL01]
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A. Joux and R. Lercier. “Chinese & Match”, an
alternative to Atkin's “Match and Sort” method used in the SEA algorithm.
Mathematics of Computation, 70(234):827-836, April 2001.
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[LM00]
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R. Lercier and F. Morain. Computing isogenies
between elliptic curves over GF(pn) using Couveignes's algorithm.
Mathematics of Computation, 69(229):351-370, January 2000.
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Proceedings
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[LRRS14]
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R. Lercier, C. Ritzenthaler, F. Rovetta, and
J. Sijsling. Parametrizing the moduli space of curves and
applications to smooth plane quartics over finite fields.
In Jung Hee Cheon and Hyang-Sook Lee, editors,
Proceedings of the Algorithmic Number Theory Symposium ANTS-XI, LMS Journal
of Computation and Mathematics, GyeongJu, South Korea, August 2014. London
Mathematical Society.
To appear.
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[BLRS13]
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R. Basson, R. Lercier, C. Ritzenthaler, and
J Sijsling. An explicit expression of the Lüroth
invariant.
In Manuel Kauers, editor, Proceedings of the
38th International Symposium on Symbolic and Algebraic Computation, ISSAC
'13, pages 31-36, New York, NY, USA, 2013. Association for Computing
Machinery.
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[LRS13]
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R. Lercier, C. Ritzenthaler, and J. Sijsling. Fast
computation of isomorphisms of hyperelliptic curves and explicit descent.
In Everett W. Howe and Kiran S. Kedlaya, editors,
Proceedings of the Tenth Algorithmic Number Theory Symposium, volume 1 of
The Open Book Series, pages 463-486. Mathematical Sciences Publishers,
2013.
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[KLR10]
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J.-G. Kammerer, R. Lercier, and
G. Renault. Encoding Points on Hyperelliptic Curves over
Finite Fields in Deterministic Polynomial Time.
In M. Joye, A. Miyaji, and A. Otsuka, editors,
Pairing-Based Cryptography - Pairing 2010, volume 6487 of Lecture Notes
in Computer Science, pages 278-297. Springer, December 2010.
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[DL10]
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C. Dunand and R. Lercier. Normal Elliptic Bases
and Torus-Based Cryptography.
In Daniel Panario Gary McGuire, Gary L. Mullen and Igor E.
Shparlinski, editors, Finite Fields: Theory and Applications,
Contemporary Mathematics, pages 137-153. American Mathematical Society,
2010.
Ninth International Conference Finite Fields and Applications.
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[JLNT09]
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A. Joux, R. Lercier, D. Naccache, and
E. Thomé. Oracle-Assisted Static Diffie-Hellman Is
Easier Than Discrete Logarithms.
In MatthewG. Parker, editor, Cryptography and
Coding, volume 5921 of Lecture Notes in Computer Science, pages 351-367.
Springer Berlin Heidelberg, December 2009.
Twelfth IMA International Conference on Cryptography and Coding
conference, Royal Agricultural College, Cirencester, UK.
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[FLRV08]
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P.-A. Fouque, R. Lercier, D. Réal, and
F. Valette. Fault Attack on Elliptic Curve with Montgomery
Ladder Implementation.
In FDTC '08. 5th Workshop on Fault Diagnosis and Tolerance in
Cryptography, pages 92-98. IEEE-CS Press, August 2008.
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[JL07]
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A. Joux and R. Lercier. Algorithmes pour
résoudre le problème du logarithme discret dans les corps finis.
In Nouvelles Méthodes Mathématiques en Cryptographie,
Fascicules Journées Annuelles, pages 23-53. Société
Mathématique de France, June 2007.
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[JLSV06]
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A. Joux, R. Lercier, N. Smart, and
F. Vercauteren. The Number Field Sieve in the Medium Prime
Case.
In C. Dwork, editor, Advances in Cryptology -
CRYPTO 2006. 26th Annual International Cryptology Conference, Santa Barbara,
California, USA, August 20-24, 2006, Proceedings, volume 4117 of Lecture
Notes in Computer Science, pages 326-344. Springer Berlin / Heidelberg,
August 2006.
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[JL06]
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A. Joux and R. Lercier. The Function Field Sieve
in the Medium Prime Case.
In S. Vaudenay, editor, Advances in Cryptology
- EUROCRYPT 2006: 24th Annual International Conference on the Theory and
Applications of Cryptographic Techniques, St. Petersburg, Russia, May 28 -
June 1, 2006. Proceedings, volume 4004 of Lecture Notes in Computer
Science, pages 254-270. Springer Berlin / Heidelberg, May 2006.
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[Ler04]
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R. Lercier. Courbes Elliptiques et cryptographie.
In Direction des Centres d'Expertise et d'Essais, number 64 in
Revue Scientifique et Technique de la Defense, pages 59-66. Délégation
générale pour l'armement, June 2004.
In french.
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[LL03]
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R. Lercier and D Lubicz. Counting Points on
Elliptic Curves over Finite Fields of Small Characteristic in Quasi Quadratic
Time.
In E. Biham, editor, Advances in Cryptology -
EUROCRPYT 2003: International Conference on the Theory and Applications of
Cryptographic Techniques, Warsaw, Poland, May 4-8, 2003. Proceedings, volume
2656 of Lecture Notes in Computer Science, pages 360-373. Springer Berlin
/ Heidelberg, May 2003.
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[JL02]
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A. Joux and R. Lercier. The Function Field Sieve
is quite special.
In C. Fieker and D.R. Kohel, editors,
Algorithmic Number Theory: 5th International Symposium, ANTS-V, Sydney,
Australia, July 7-12, 2002. Proceedings, volume 2369 of Lecture Notes in
Computer Science, pages 431-445. Springer Berlin / Heidelberg, July 2002.
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[LM98]
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R. Lercier and F. Morain. Algorithms for computing
isogenies between elliptic curves.
In D.A. Buell and J.T. Teitelbaum, editors,
Computational Perspectives on Number Theory: Proceedings of a Conference in
Honor of A. O. L. Atkin, volume 7 of AMS/IP Studies in Advanced
Mathematics, pages 77-96, Providence, 1998. American Mathematical Society
& Internationnal Press.
Held in 1995 at the University of Illinois at Chicago.
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[Ler97]
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R. Lercier. Finding Good Random Elliptic Curves
for Cryptosystems Defined Over GF(2n).
In W. Fumy, editor, Advances in Cryptology -
EUROCRYPT '97: International Conference on the Theory and Application of
Cryptographic Techniques, Konstanz, Germany, May 1997. Proceedings, volume
1233 of Lecture Notes in Computer Science, pages 379-392. Springer Berlin
/ Heidelberg, May 1997.
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[Ler96]
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R. Lercier. Computing isogenies in GF(2n).
In H. Cohen, editor, Algorithmic Number Theory:
Second International Symposium, ANTS-II Talence, France, May 18-23, 1996
Proceedings, volume 1122 of Lecture Notes in Computer Science, pages
197-212. Springer Berlin / Heidelberg, May 1996.
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[LM95]
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R. Lercier and F. Morain. Counting the Number of
Points on Elliptic Curves over Finite Fields: Strategies and Performances.
In L.C. Guillou and J.-J. Quisquater, editors,
Advances in Cryptology - EUROCRYPT '95: International Conference on the
Theory and Application of Cryptographic Techniques, Saint-Malo, France, May
1995. Proceedings, volume 921 of Lecture Notes in Computer Science, pages
79-94. Springer Berlin / Heidelberg, May 1995.
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Books
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[JL11]
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A. Joux and R. Lercier. Encyclopedia of
Cryptography and Security.
Chapter Number Field Sieve for DLP, pages 867-873.
Springer, 2011.
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[CF06]
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H. Cohen and G. Frey, editors. Handbook of
Elliptic and Hyperelliptic Curve Cryptography.
Chapter 17, Point Counting on Elliptic and Hyperelliptic
Curves, R. Lercier, D. Lubicz and F. Vercauteren, pages 407-449.
Discrete Mathematics and its Applications. Chapman & Hall/CRC, 2006.
K.H. Rosen, series editor.
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Manuscripts
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[JL06]
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A. Joux and R. Lercier. Counting points on
elliptic curves in medium characteristic.
Cryptology ePrint Archive, Report 2006/176, May 2006.
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[Ler04]
|
R. Lercier. Contributions à l'arithmétique
de la cryptographie.
Manuscript submitted for the “Habilitation à diriger des
recherches” (in french), Université d'Aix-Marseille II, U.F.R. de
Science. Luminy campus, Marseille, November 2004.
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[JL04]
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E. Jaulmes and R. Lercier. FRMAC, a Fast
Randomized Message Authentication Code.
Cryptology ePrint Archive, Report 2004/166, July 2004.
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[Ler97]
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R. Lercier. Algorithmique des Courbes
Elliptiques dans les Corps Finis.
PhD thesis, École polytechnique, Palaiseau, June 1997.
In french.
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[CL96]
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F. Chabaud and R. Lercier. ZEN, a new toolbox
for computing in finite extension of finite rings. User's manual.
1996.
Sourceforge project.
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[LM95]
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R. Lercier and F. Morain. Counting points on
elliptic curves over GF(pn) using Couveignes's algorithm.
Research report LIX/RR/95/09, Laboratoire d'Informatique de
l'École polytechnique (LIX), 1995.
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[Ler93]
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R. Lercier. Factoriser des entiers par la
méthode des courbes elliptiques.
Master's thesis, École polytechnique, Palaiseau, July 1993.
Master memoir (in french).
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