Part of the Lecture Notes in Computer Science book series (LNCS, volume 2020)
Analysis of the Weil Descent Attack of Gaudry, Hess and Smart
We analyze the Weil descent attack of Gaudry, Hess and Smart  on the elliptic curve discrete logarithm problem for elliptic curves defined over finite fields of characteristic two.
Unable to display preview. Download preview PDF.
- 1.L. Adleman, J. DeMarrais and M. Huang, “A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields”, Algorithmic Number Theory, LNCS 877, 1994, 28–40.Google Scholar
- 3.A. Enge, “The extended Euclidean algorithm on polynomials, and the efficiency of hyperelliptic cryptosystems”, Designs, Codes and Cryptography, to appear.Google Scholar
- 4.A. Enge and P. Gaudry, “A general framework for subexponential discrete logarithm algorithms”, Rapport de Recherche Lix/RR/00/04, June 2000. Available from http://ultralix.polytechnique.fr/Labo/Pierrick.Gaudry/papers.html
- 5.G. Frey, “How to disguise an elliptic curve (Weil descent) ”, Talk at ECC’ 98, Waterloo, 1998. Slides available from http://www.cacr.math.uwaterloo.ca/conferences/1998/ecc98/slides.html
- 6.G. Frey, “Applications of arithmetical geometry to cryptographic constructions”, Proceedings of the Fifth International Conference on Finite Fields and Applications, to appear. Also available from http://www.exp-math.uni-essen.de/zahlentheorie/preprints/Index.html
- 7.G. Frey and H. Rück, “A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves”, Mathematics of Computation, 62 (1994), 865–874.Google Scholar
- 9.R. Gallant, R. Lambert and S. Vanstone, “Improving the parallelized Pollard lambda search on binary anomalous curves”, to appear in Mathematics of Computation.Google Scholar
- 11.P. Gaudry, F. Hess and N. Smart, “Constructive and destructive facets of Weil descent on elliptic curves”, preprint, January 2000. Available from http://ultralix.polytechnique.fr/Labo/Pierrick.Gaudry/papers.html
- 12.Internet Engineering Task Force, The OAKLEY Key Determination Protocol, IETF RFC 2412, November 1998.Google Scholar
- 14.A. Menezes, T. Okamoto and S. Vanstone, “Reducing elliptic curve logarithms to logarithms in a finite field”, tiIEEE Transactions on Information Theory, 39 (1993), 1639–1646.Google Scholar
- 15.National Institute of Standards and Technology, Digital Signature Standard, FIPS Publication 186-2, February 2000.Google Scholar
© Springer-Verlag Heidelberg 1999