Publications and Preprints

Publications

• Complex multiplication and canonical lifts in Algebraic geometry and its applications, Proceedings of the first SAGA conference (Papeete, 2007), Number Theory and its Applications, vol. 5, 67-83, 2008.
• Higher dimensional 3-adic CM construction with R. Carls and D. Lubicz, Journal of Algebra, 319, no. 3, 971-1006, 2008.
• The Weierstrass subgroup of a curve has maximal rank, with M. Girard and C. Ritzenthaler, Bulletin of the London Mathematical Society 38, Issue 06, 925-931, 2006.
• The 2-adic CM method for genus 2 curves with application to cryptography, with P. Gaudry, T. Houtmann, C. Ritzenthaler, and A. Weng, Proceedings of Asiacrypt 2006 (Shanghai, 2006), LNCS 4284, 114-129, 2006. [Springer link]
• Classification of genus 3 curves in special strata of the moduli space, with M. Girard, Proceedings of ANTS VII (Berlin, 2006), LNCS 4076, 346-360, 2006. [Springer link]
• Efficiently computable endomorphisms for hyperelliptic curves, with B. Smith, Proceedings of ANTS VII (Berlin, 2006), LNCS 4076, 495-509, 2006. [Springer link]
• 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. [Springer link] For comparative analysis (and improvements to our formulae), see the Explicit Formulas Database web page of Bernstein and Lange on hyperelliptic.org.
• The AGM-X₀(N) Heegner point lifting algorithm and elliptic curve point counting, Proceedings of Asiacrypt 2003 (Taipei), LNCS 2894, 124-136, 2003. [Springer link]
• Fundamental domains for Shimura curves, with Helena Verrill, Journal of Number Theory of Bordeaux, 15, no. 1, 205-222, 2003.
• Rational groups of elliptic curves suitable for cryptography, Proceedings of Cryptography and computational number theory (Singapore, 1999), Progress in Computer Science and Applied Logic, 20, 69--80, 2001.
• Component groups of quotients of J₀(N) with William Stein. Proceedings of ANTS IV (Leiden, 2000), LNCS 1838, 405-412, 2000. [Springer link]
• On exponential sums and group generators for elliptic curves over finite fields, with Igor Shparlinski. Proceedings of ANTS IV, (Leiden, 2000), LNCS 1838, 405-412, 2000. [Springer link]
• Hecke module structure of quaternions. Proceedings of Class Field Theory - Centenary and Prospect (Tokyo, 1998), K. Miyake, ed., Advanced Studies in Pure Mathematics, 30, 177-196, 2000.
• Split group codes, with Cunsheng Ding and San Ling. IEEE Transactions on Information Theory 46, no. 2, 485--495, 2000.
• Elementary 2-group character codes, with Cunsheng Ding and San Ling, IEEE Transactions on Information Theory, 46, no. 1, 280-283, 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 SETA'98 (Singapore, 1998), 308-317, 1999.
• Endomorphism rings of elliptic curves over finite fields. Thesis, University of California, Berkeley, December, 1996.

Preprints

• The p-adic CM-method for genus 2, with P. Gaudry, T. Houtmann, C. Ritzenthaler, and A. Weng, 2005.
• Constructive and destructive facets of torus-based cryptography, 2004.
• Computing modular curves via quaternions, based on talk at Computational Algebraic Number Theory, Sydney, December 1997.

Books

• Cryptography, introductory text on cryptography based on teaching (see also MATH3024 and MATH3925), with exercises in SAGE, 2007.
  This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported License.
• Algorithmic Number Theory, Proceedings of ANTS V (Sydney, 2002), editted with C. Fieker, LNCS 2369, 2002.

Slides and shorter notes from talks

• Complex multiplication and canonical lifts Slides from SAGA 2007, 2007.
• 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.