Publications and Preprints
Publications
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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.
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Higher dimensional 3-adic CM construction
with R. Carls and D. Lubicz,
Journal of Algebra,
319, no. 3, 971-1006, 2008.
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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.
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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]
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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]
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Efficiently computable endomorphisms for hyperelliptic curves,
with B. Smith, Proceedings of
ANTS VII (Berlin, 2006),
LNCS 4076, 495-509, 2006.
[Springer link]
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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.
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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]
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Fundamental domains for Shimura curves, with Helena Verrill,
Journal of Number Theory of Bordeaux, 15, no. 1, 205-222, 2003.
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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.
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Component groups of quotients of J0(N)
with William Stein. Proceedings of
ANTS IV (Leiden, 2000),
LNCS 1838, 405-412, 2000.
[Springer link]
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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.
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Split group codes, with Cunsheng Ding and San Ling.
IEEE Transactions on Information Theory 46, no. 2, 485--495, 2000.
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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
Books
Slides and shorter notes from talks
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Complex multiplication and canonical lifts
Slides from
SAGA 2007, 2007.
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Construction of CM moduli by p-adic lifting,
Notes from a talk at the 50th annual meeting of the Australian
Mathematical Society, 2006.
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Classification of genus 3 curves in special strata of the moduli space,
slides from talk at ANTS VII in Berlin, 24 July 2006.
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Construction p-adique des invariant CM des courbes
de genre 2,
slides from talk at Université Toulouse Le Mirail,
12 December 2005.
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Tores algébriques et jacobiennes generalisees
en cryptographie, slides from talk at Institut
Mathématique de Luminy, 8 December 2005.
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Constructive p-adic CM for genus 2 curves,
slides from talk at Center for Communications Research,
6 October 2005.
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An l-adic CM method for genus 2,
slides from talk at the Journées Arithmétiques,
July 2005.
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Introduction to magma and applications,
slides from talk at the
African Institute for the Mathematical Sciences, 2005.
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The AGM-X0(N) Algorithm,
Slides from presentation at Asiacrypt'03.
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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.