Research Articles and Preprints

Publications and preprints

• Higher dimensional 3-adic CM construction with R. Carls and D. Lubicz, preprint 2006.
• The 2-adic CM method for genus 2 curves with application to cryptography, to appear in Asiacrypt 2006 (Shanghai, 2006).
• The Weierstrass subgroup of a curve has maximal rank, with M. Girard and C. Ritzenthaler (to appear in Bulletin of the London Mathematical Society), 2006.
• Classification of genus 3 curves in special strata of the moduli space, with M. Girard, Proceedings of ANTS VII (Berlin), LNCS 4076, 346-360, 2006.
• Efficiently computable endomorphisms for hyperelliptic curves, with B. Smith, Proceedings of ANTS VII (Berlin), LNCS 4076, 495-509, 2006.
• Efficient scalar multiplication by isogeny decompositions, with C. Doche and T. Icart, Proceedings of Public Key Cryptography 2006 (New York), LNCS 3958, 191-206, 2006.
• The p-adic CM-method for genus 2, with P. Gaudry, T. Houtmann, C. Ritzenthaler, and A. Weng, preprint, 2005.
• Constructive and destructive facets of torus-based cryptography, preprint, 2004.
• The AGM-X₀(N) Heegner point lifting algorithm and elliptic curve point counting, [SpringerLink], Proceedings of Asiacrypt 2003 (Taipei), LNCS 2894, 2003.
• Fundamental domains for Shimura curves, with Helena Verrill. Journal of Number Theory of Bordeaux, 15, 2003.
• Rational groups of elliptic curves suitable for cryptography, Cryptography and computational number theory (Singapore, 1999), 69--80, Progr. Comput. Sci. Appl. Logic, 20, 2001.
• Component groups of quotients of J₀(N) with William Stein. Proceedings of ANTS IV, Leiden University, LNCS 1838, 2000.
• On exponential sums and group generators for elliptic curves over finite fields, with Igor Shparlinski. Proceedings of ANTS IV, Leiden University, July 2000.
• Hecke module structure of quaternions. Proceedings of Class Field Theory - Centenary and Prospect (Waseda University, Tokyo, June, 1998), K. Miyake, ed., 2000.
• Split group codes, with Cunsheng Ding and San Ling. IEEE Transactions on Information Theory, 46 (2000), no. 2, 485--495.
• Elementary 2-group character codes, with Cunsheng Ding and San Ling. IEEE Transactions on Information Theory, January 2000.
• Explicit sequence expansions, with San Ling and Chaoping Xing. In Sequences and their Applications, C. Ding, T. Helleseth, and H. Niederreiter, eds. Proceedings of the International Conference on Sequences and their Applications. National University of Singapore. 14-17 December 1998.
• Computing modular curves via quaternions. Based on talk at the CANT conference in Sydney, December, 1997.
• Endomorphism rings of elliptic curves over finite fields. Thesis, University of California, Berkeley, December, 1996.

Notes from Talks

• Construction of CM moduli by p-adic lifting, Notes from a talk at the 50th annual meeting of the Australian Mathematical Society, 2006.
• Classification of genus 3 curves in special strata of the moduli space, slides from talk at ANTS VII in Berlin, 24 July 2006.
• Construction p-adique des invariant CM des courbes de genre 2, slides from talk at Université Toulouse Le Mirail, 12 December 2005.
• Tores algébriques et jacobiennes generalisees en cryptographie, slides from talk at Institut Mathématique de Luminy, 8 December 2005.
• Constructive p-adic CM for genus 2 curves, slides from talk at Center for Communications Research, 6 October 2005.
• An l-adic CM method for genus 2, slides from talk at the Journées Arithmétiques, July 2005.
• Introduction to magma and applications, slides from talk at the African Institute for the Mathematical Sciences, 2005.
• The AGM-X₀(N) Algorithm, Slides from presentation at Asiacrypt'03.
• On invariants of Shimura curves. Slides from a talk on Shimura curves at the Arithmetic Geometry worshop at MSRI, December 2000.
• Part I (Magma language) and Part II (Number theoretic applications). Slides from a presentation on the magma computer language and selected applications in number theory, October 2000.
• Coding theory: algebraic geometry of linear algebra. Rough notes of talk algebraic geometric codes, National University of Singapore, April, 1997.
• Cyclotomic polynomials and base b representations of integers. Solution to Solomon Golomb's puzzle "Two-digit base b representations," IEEE Information Theory Society Newsletter, March 1997.
• Sumas de cuadrados. Rough notes of talk at the Instituto de Matemáticas de la UNAM in Morelia, México, February, 1997.