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Algorithmic Number Theory

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Cover of 'Algorithmic Number Theory'

Table of Contents

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    Book Overview
  2. Altmetric Badge
    Chapter 1 Running Time Predictions for Factoring Algorithms
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    Chapter 2 A New Look at an Old Equation
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    Chapter 3 Abelian Varieties with Prescribed Embedding Degree
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    Chapter 4 Almost Prime Orders of CM Elliptic Curves Modulo p
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    Chapter 5 Efficiently Computable Distortion Maps for Supersingular Curves
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    Chapter 6 On Prime-Order Elliptic Curves with Embedding Degrees k  = 3, 4, and 6
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    Chapter 7 Computing in Component Groups of Elliptic Curves
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    Chapter 8 Some Improvements to 4-Descent on an Elliptic Curve
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    Chapter 9 Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields
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    Chapter 10 Faster Multiplication in GF(2)[ x ]
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    Chapter 11 Predicting the Sieving Effort for the Number Field Sieve
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    Chapter 12 Improved Stage 2 to P ± 1 Factoring Algorithms
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    Chapter 13 Shimura Curve Computations Via K3 Surfaces of Néron–Severi Rank at Least 19
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    Chapter 14 K3 Surfaces of Picard Rank One and Degree Two
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    Chapter 15 Number Fields Ramified at One Prime
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    Chapter 16 An Explicit Construction of Initial Perfect Quadratic Forms over Some Families of Totally Real Number Fields
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    Chapter 17 Functorial Properties of Stark Units in Multiquadratic Extensions
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    Chapter 18 Enumeration of Totally Real Number Fields of Bounded Root Discriminant
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    Chapter 19 Computing Hilbert Class Polynomials
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    Chapter 20 Computing Zeta Functions in Families of C a , b Curves Using Deformation
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    Chapter 21 Computing L-series of hyperelliptic curves
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    Chapter 22 Point Counting on Singular Hypersurfaces
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    Chapter 23 Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors
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    Chapter 24 Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian
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    Chapter 25 Computing Hilbert Modular Forms over Fields with Nontrivial Class Group
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    Chapter 26 Hecke Operators and Hilbert Modular Forms
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    Chapter 27 A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm
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    Chapter 28 An Improved Multi-set Algorithm for the Dense Subset Sum Problem
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    Chapter 29 On the Diophantine Equation x 2  + 2 α 5 β 13 γ  =  y n
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    Chapter 30 Non-vanishing of Dirichlet L -functions at the Central Point
Attention for Chapter 10: Faster Multiplication in GF(2)[ x ]
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Chapter title
Faster Multiplication in GF(2)[ x ]
Chapter number 10
Book title
Algorithmic Number Theory
Published by
Springer, Berlin, Heidelberg, May 2008
DOI 10.1007/978-3-540-79456-1_10
Book ISBNs
978-3-54-079455-4, 978-3-54-079456-1
Authors

Richard P. Brent, Pierrick Gaudry, Emmanuel Thomé, Paul Zimmermann, Brent, Richard P., Gaudry, Pierrick, Thomé, Emmanuel, Zimmermann, Paul

Mendeley readers

Mendeley readers

The data shown below were compiled from readership statistics for 10 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country Count As %
United States 1 10%
Unknown 9 90%

Demographic breakdown

Readers by professional status Count As %
Student > Ph. D. Student 3 30%
Researcher 3 30%
Professor 1 10%
Other 1 10%
Student > Master 1 10%
Other 1 10%
Readers by discipline Count As %
Computer Science 5 50%
Physics and Astronomy 2 20%
Mathematics 1 10%
Medicine and Dentistry 1 10%
Engineering 1 10%
Other 0 0%