Publications

Works in Progress

Refereed Publications

• Pairings on Hyperelliptic Curves.
  In WIN---Women in Numbers: Research Directions in Number Theory, Fields Institute Communications, vol. 60, Amer. Math. Soc., Providence, RI, 2011, pp. 87-120 (with Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm, Kirsten Eisenträger, and Katherine Stange).
  

• A Taxonomy of Pairing-friendly Elliptic Curves.
  Journal of Cryptology, 23 (2010), 224-280 (with David Freeman and Michael Scott).
  DOI: 10.1007/s00145-009-9048-z
  

• On Prime-order Elliptic Curves with Embedding Degrees k=3,4 and 6.
  Algorithmic Number Theory -- ANTS VIII, LNCS 5011, Springer 2008, pages 102-117 (with Koray Karabina).
  

• Cryptographic Implications of Hess' Generalized GHS Attack.
  Applicable Algebra in Engineering, Communication and Computing, 16 (2006), 439-460 (with Alfred Menezes).

• An Elliptic Curve Trapdoor System.
  Journal of Cryptology, 19 (2006), 115-133.
  (Extended abstract in: Fields Institute Communications Series, 41 (2004), 341-352.)
  

• Optimized Baby Step-Giant Step Methods.
  The Journal of the Ramanujan Mathematical Society, 20 (2005), 27-58 (with Andreas Stein).
  

• Point Counting on Picard Curves in Large Characteristic.
  Mathematics of Computation, 74 (2005), 1983-2005 (with Mark Bauer and Annegret Weng).
  

• Weak Fields for ECC.
  Topics in Cryptology -- CT-RSA 2004, LNCS 2964, Springer 2004, pages 366-386 (with Alfred Menezes and Annegret Weng).
  

• Computing Discrete Logarithms with the Parallelized Kangaroo Method.
  Discrete Applied Mathematics, 130 (2003), 61-82.
  

• On some Attacks on Multi-prime RSA.
  Selected Areas in Cryptography -- 9th Annual International Workshop, SAC 2002, LNCS 2595, Springer 2003, pages 385-404 (with M Jason Hinek and Mo King Low).
  

• Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree .
  LMS Journal of Computation and Mathematics, 5 (2002), 127-174 (with Markus Maurer and Alfred Menezes). MR 1 942 257.
  An earlier, shorter version appeared in Proceedings of Indocrypt 2001, LNCS 2247, Springer 2001, pages 195-213. MR 1 934 497.
  

• Factoring N= pq^2 with the Elliptic Curve Method.
  Algorithmic Number Theory -- ANTS V, LNCS 2369, Springer 2002, pages 475-490 (with Peter Ebinger).
  Supplement: On the Jacobi Symbol Continuation of ECM . 14 pages.
  

• Explicit Bounds and Heuristics on Class Numbers in Hyperelliptic Function Fields.
  Mathematics of Computation, 71 (2002), 837-861 (with Andreas Stein).
  MR 2002k:11210.
  

• The Parallelized Pollard Kangaroo Method in Real Quadratic Function Fields.
  Mathematics of Computation, 71 (2002), 793-814 (with Andreas Stein).
  MR 2002k:11227.
  

• Square-root Algorithms for the Discrete Logarithm Problem (A Survey).
  In: Public-Key Cryptography and Computational Number Theory, Walter de Gruyter, Berlin - New York 2001, pages 283-301.
  MR 2003c:11156.
  

• On Random Walks for Pollard's Rho Method
  Mathematics of Computation 70 (2001), pages 809-825.
  MR 2001g:11194.
  

• A Note on Shanks's Chains of Primes.
  Proceedings of ANTS IV, LNCS 1838, Springer 2000, pages 563-580 (with Hugh Williams).
  MR 2002k:11228.
  

• Baby-Step Giant-Step Algorithms for Non-Uniform Distributions.
  Proceedings of ANTS IV, LNCS 1838, Springer 2000, pages 153-168 (with Simon R. Blackburn).
  MR 2002i:11127.
  

• Analysis of the Xedni Calculus Attack
  Designs, Codes and Cryptography 20 (2000), pages 41 - 64 (with Michael J. Jacobson, Neal Koblitz, Joseph H. Silverman, and Andreas Stein).
  MR 2001b:14043.
  

• The Pohlig-Hellman Method Generalized for Group Structure Computation.
  J. Symbolic Computation 27 (1999), pages 521-534.
  MR 2000f:20090.
  

• A Problem Concerning a Character Sum.
  Experimental Mathematics 8 (1999), pages 63-72 (with Hugh Williams).
  MR 2000b:11102.
  

• A Problem Concerning a Character Sum (Extended Abstract).
  Proceedings of ANTS III, LNCS 1423, Springer 1998, pages 351-357 (with Hugh Williams).
  MR 1 726 083.
  

• Speeding up Pollard's Rho Method for Computing Discrete Logarithms.
  Proceedings of ANTS III, LNCS 1423, Springer 1998, pages 541-553.
  MR 2000j:11199.
  

• A Space Efficient Algorithm for Group Structure Computation.
  Mathematics of Computation 67 (1998), pages 1637-1663.
  MR 99a:11146.
  

• On some Computational Problems in Finite Abelian Groups.
  Mathematics of Computation 66 (1997), pages 1663 - 1687 (with Johannes Buchmann and Michael J. Jacobson).
  MR 98a:11185.
  

Other Work

• Pairing-friendly elliptic curves.
  Entry for the second edition of the "Encyclopedia of Cryptography and Security", edited by Henk van Tilborg and Sushil Jajodia.
  5 pages, 2009.
  

• Computing Discrete Logarithms in Arithmetic Progressions.
  2 pages, 1999.
  

• Some Arithmetic Properties of Shanks' Generalized Euler and Class Numbers.
  (With Hugh Williams). 20 pages.
  

• Growth and Range Conditions for the Laplace Representation of Vector-Valued Functions.
  Beiträge zur Angewandten Analysis und Informatik: Helmut Brakhage zu Ehren, Eberhard Schock (ed.), Aachen, Shaker, 1994 (with Lutz Weis).
  MR 96b:44002.
  

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