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Algorithmic Number Theory

8th International Symposium, ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings

  • Conference proceedings
  • © 2008

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Editors:
  1. Alfred J. Poorten
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  2. Andreas Stein
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Part of the book series: Lecture Notes in Computer Science (LNCS, volume 5011)

Part of the book sub series: Theoretical Computer Science and General Issues (LNTCS)

Included in the following conference series:

Conference proceedings info: ANTS 2008.

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Table of contents (30 papers)

  1. Front Matter

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  2. Invited Papers

    1. Running Time Predictions for Factoring Algorithms

      • Ernie Croot, Andrew Granville, Robin Pemantle, Prasad Tetali
      Pages 1-36

    2. A New Look at an Old Equation

      • R. E. Sawilla, A. K. Silvester, H. C. Williams
      Pages 37-59

  3. Elliptic Curves Cryptology and Generalizations

    1. Abelian Varieties with Prescribed Embedding Degree

      • David Freeman, Peter Stevenhagen, Marco Streng
      Pages 60-73

    2. Almost Prime Orders of CM Elliptic Curves Modulo p

      • Jorge Jiménez Urroz
      Pages 74-87

    3. Efficiently Computable Distortion Maps for Supersingular Curves

      • Katsuyuki Takashima
      Pages 88-101

    4. On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6

      • Koray Karabina, Edlyn Teske
      Pages 102-117

  4. Arithmetic of Elliptic Curves

    1. Computing in Component Groups of Elliptic Curves

      • J. E. Cremona
      Pages 118-124

    2. Some Improvements to 4-Descent on an Elliptic Curve

      • Tom Fisher
      Pages 125-138

    3. Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields

      • Thotsaphon Thongjunthug
      Pages 139-152

    4. Faster Multiplication in GF(2)[x]

      • Richard P. Brent, Pierrick Gaudry, Emmanuel Thomé, Paul Zimmermann
      Pages 153-166

  5. Integer Factorization

    1. Predicting the Sieving Effort for the Number Field Sieve

      • Willemien Ekkelkamp
      Pages 167-179

    2. Improved Stage 2 to P ± 1 Factoring Algorithms

      • Peter L. Montgomery, Alexander Kruppa
      Pages 180-195

  6. K3 Surfaces

    1. Shimura Curve Computations Via K3 Surfaces of Néron–Severi Rank at Least 19

      • Noam D. Elkies
      Pages 196-211

    2. K3 Surfaces of Picard Rank One and Degree Two

      • Andreas-Stephan Elsenhans, Jörg Jahnel
      Pages 212-225

  8. Point Counting

    1. Computing Hilbert Class Polynomials

      • Juliana Belding, Reinier Bröker, Andreas Enge, Kristin Lauter
      Pages 282-295
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About this book

This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.

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