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Reynald Lercier — Full publication list

Numbered chronologically, most recent first.

  1. Elliptic Butterflies, avec J.-M. Couveignes. Journal of Complexity, 95:102046, 2026. DOI arXiv:2510.27375
  2. Reduction of Plane Quartics and Cayley Octads, avec R. van Bommel, J. Docking, V. Dokchitser, and E. Lorenzo García. Foundations of Computational Mathematics, 26:1425–1496, 2026. DOI arXiv:2309.17381
  3. Functionality for isomorphism classes of curves and hypersurfaces, avec T. Bouchet, J. Sijsling, and C. Ritzenthaler. Preprint, 2026. arXiv:2102.04372
  4. Reduction of Plane Quartics and Dixmier–Ohno Invariants, avec R. van Bommel, J. Docking, and E. Lorenzo García. Research in Number Theory, 11:41, 2025. DOI arXiv:2401.13902
  5. Stable models of plane quartics with hyperelliptic reduction, avec E. Lorenzo García and C. Ritzenthaler. Contemporary Mathematics, 770:223–237, 2021. DOI arXiv:1906.00795
  6. Reduction type of smooth plane quartics, avec Q. Liu, E. Lorenzo García, and C. Ritzenthaler. Algebra & Number Theory, 15(6):1429–1468, 2021. DOI arXiv:1803.05816
  7. Fast computation of elliptic curve isogenies in characteristic two, avec X. Caruso and E. Eid. Journal of the London Mathematical Society, 104(4):1901–1929, 2021. DOI arXiv:2003.06367
  8. Reconstructing Plane Quartics from Their Invariants, avec C. Ritzenthaler and J. Sijsling. Discrete & Computational Geometry, 63(1):73–113, 2020. DOI arXiv:1606.05594
  9. Distributions of Traces of Frobenius for Smooth Plane Curves over Finite Fields, avec C. Ritzenthaler, F. Rovetta, J. Sijsling, and B. Smith. Experimental Mathematics, 28(1):39–48, 2019. DOI arXiv:1510.05601
  10. Grøstl Distinguishing Attack: A New Rebound Attack of an AES-like Permutation, avec V. Cauchois and C. Gomez. IACR Transactions on Symmetric Cryptology, 2017(3):1–23, 2017. DOI ePrint 2017/508
  11. Plane quartics over ℚ with complex multiplication, avec P. Kılıçer, H. Labrande, C. Ritzenthaler, J. Sijsling, and M. Streng. Preprint, 2017 (last revised 2022). DOI arXiv:1701.06489
  12. Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group, avec C. Ritzenthaler and J. Sijsling. Mathematics of Computation, 85(300):2011–2045, 2016. DOI arXiv:1301.0695
  13. Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields, avec C. Ritzenthaler, F. Rovetta, and J. Sijsling. LMS Journal of Computation and Mathematics, 17(Theory):128–147, 2014 (Proceedings ANTS-XI). DOI arXiv:1403.0562
  14. The geometry of some parameterizations and encodings, avec J.-M. Couveignes. Advances in Mathematics of Communications, 8(4):437–458, 2014. DOI arXiv:1310.1013
  15. Fast computation of isomorphisms of hyperelliptic curves and explicit descent, avec C. Ritzenthaler and J. Sijsling. In Proceedings of ANTS X, Open Book Series 1, pages 463–486. MSP, 2013. DOI arXiv:1203.5440
  16. An explicit expression of the Lüroth invariant, avec R. Basson, C. Ritzenthaler, and J. Sijsling. In ISSAC '13, pages 31–36. ACM, 2013. DOI arXiv:1211.1327
  17. Elliptic periods and primality proving, avec T. Ezome. Journal of Number Theory, 133(1):343–368, 2013. DOI arXiv:0810.2853 (extended version)
  18. Fast construction of irreducible polynomials over finite fields, avec J.-M. Couveignes. Israel Journal of Mathematics, 194:77–105, 2013. DOI arXiv:0905.1642
  19. A faster pseudo-primality test, avec J.-M. Couveignes and T. Ezome. Rendiconti del Circolo Matematico di Palermo, 61:261–278, 2012. DOI arXiv:1204.1657
  20. Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects, avec C. Ritzenthaler. Journal of Algebra, 372:595–636, 2012. DOI arXiv:1111.4152
  21. Number Field Sieve for DLP, avec A. Joux. In Encyclopedia of Cryptography and Security (2nd ed.), pages 867–873. Springer, 2011. (book chapter — see also Books & chapters on the homepage) DOI
  22. Normal Elliptic Bases and Torus-Based Cryptography, avec C. Dunand. In Finite Fields: Theory and Applications, Contemporary Mathematics, pages 137–153. AMS, 2010. DOI PDF
  23. Encoding Points on Hyperelliptic Curves over Finite Fields in Deterministic Polynomial Time, avec J.-G. Kammerer and G. Renault. In Pairing 2010, LNCS 6487, pages 278–297. Springer, 2010. DOI arXiv:1005.1454
  24. Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms, avec A. Joux, D. Naccache, and E. Thomé. In Cryptography and Coding (IMACC 2009), LNCS 5921, pages 351–367. Springer, 2009. DOI PDF
  25. Elliptic periods for finite fields, avec J.-M. Couveignes. Finite Fields and Their Applications, 15(1):1–22, 2009. DOI arXiv:0802.0165
  26. Fault Attack on Elliptic Curve with Montgomery Ladder Implementation, avec P.-A. Fouque, D. Réal, and F. Valette. In FDTC '08, pages 92–98. IEEE-CS, 2008. DOI PDF
  27. Galois invariant smoothness basis, avec J.-M. Couveignes. Series on Number Theory and Its Applications, 5:142–167, 2008. DOI arXiv:0802.0282
  28. On Elkies subgroups of ℓ-torsion points in elliptic curves defined over a finite field, avec T. Sirvent. Journal de Théorie des Nombres de Bordeaux, 20(3):783–797, 2008. DOI arXiv:0809.2774
  29. Algorithmes pour résoudre le problème du logarithme discret dans les corps finis (in French), avec A. Joux. In Nouvelles Méthodes Mathématiques en Cryptographie, pages 23–53. SMF, 2007. PDF
  30. Counting points on elliptic curves in medium characteristic, avec A. Joux. Cryptology ePrint Archive, Report 2006/176. ePrint 2006/176
  31. Point Counting on Elliptic and Hyperelliptic Curves, avec D. Lubicz and F. Vercauteren. Chapter 17 in Handbook of Elliptic and Hyperelliptic Curve Cryptography, pages 407–449. Chapman & Hall/CRC, 2006 (2nd ed. 2012). (book chapter — see also Books & chapters on the homepage) DOI
  32. A Quasi Quadratic Time Algorithm for Hyperelliptic Curve Point Counting, avec D. Lubicz. The Ramanujan Journal, 12(3):399–423, 2006. DOI PDF
  33. The Function Field Sieve in the Medium Prime Case, avec A. Joux. In EUROCRYPT 2006, LNCS 4004, pages 254–270. Springer, 2006. DOI PDF
  34. The Number Field Sieve in the Medium Prime Case, avec A. Joux, N. Smart, and F. Vercauteren. In CRYPTO 2006, LNCS 4117, pages 326–344. Springer, 2006. DOI PDF
  35. FRMAC, a Fast Randomized Message Authentication Code, avec E. Jaulmes. Cryptology ePrint Archive, Report 2004/166. ePrint 2004/166
  36. Contributions à l'arithmétique de la cryptographie (in French). Habilitation à diriger des recherches, Université d'Aix-Marseille II, 2004. HAL tel-01101947
  37. Courbes Elliptiques et cryptographie (in French). Revue Scientifique et Technique de la Défense, (64):59–66, 2004. PDF
  38. Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method, avec A. Joux. Mathematics of Computation, 72(242):953–967, 2003. DOI PDF
  39. Counting Points on Elliptic Curves over Finite Fields of Small Characteristic in Quasi Quadratic Time, avec D. Lubicz. In EUROCRYPT 2003, LNCS 2656, pages 360–373. Springer, 2003. DOI PDF
  40. The Function Field Sieve is quite special, avec A. Joux. In ANTS-V, LNCS 2369, pages 431–445. Springer, 2002. DOI PDF
  41. "Chinese & Match", an alternative to Atkin's "Match and Sort" method used in the SEA algorithm, avec A. Joux. Mathematics of Computation, 70(234):827–836, 2001. DOI PDF
  42. Computing isogenies between elliptic curves over GF(pn) using Couveignes's algorithm, avec F. Morain. Mathematics of Computation, 69(229):351–370, 2000. DOI PDF
  43. Algorithms for computing isogenies between elliptic curves, avec F. Morain. In Computational Perspectives on Number Theory, AMS/IP Studies in Advanced Mathematics 7, pages 77–96. AMS & International Press, 1998. DOI PDF
  44. Algorithmique des courbes elliptiques dans les corps finis (in French). PhD thesis, École polytechnique, 1997. HAL tel-01101949
  45. Finding Good Random Elliptic Curves for Cryptosystems Defined Over GF(2n). In EUROCRYPT '97, LNCS 1233, pages 379–392. Springer, 1997. DOI PDF
  46. Computing isogenies in GF(2n). In ANTS-II, LNCS 1122, pages 197–212. Springer, 1996. DOI PDF
  47. Counting points on elliptic curves over GF(pn) using Couveignes's algorithm, avec F. Morain. Research report LIX/RR/95/09, LIX, École polytechnique, 1995. PDF
  48. Counting the Number of Points on Elliptic Curves over Finite Fields: Strategies and Performances, avec F. Morain. In EUROCRYPT '95, LNCS 921, pages 79–94. Springer, 1995. DOI PDF
  49. Factoriser des entiers par la méthode des courbes elliptiques (in French). Master's thesis, École polytechnique, 1993. PDF