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Algorithmic Number Theory

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Cover of 'Algorithmic Number Theory'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Putting the Hodge and Tate Conjectures to the Test
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    Chapter 2 Curves of Genus 3 with a Group of Automorphisms Isomorphic to S3
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    Chapter 3 Learning with Errors over Rings
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    Chapter 4 Lattices and Spherical Designs
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    Chapter 5 Fixed Points for Discrete Logarithms
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    Chapter 6 Explicit Coleman Integration for Hyperelliptic Curves
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    Chapter 7 Smallest Reduction Matrix of Binary Quadratic Forms
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    Chapter 8 Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields
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    Chapter 9 On the Use of the Negation Map in the Pollard Rho Method
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    Chapter 10 An O(M(n) logn) Algorithm for the Jacobi Symbol
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    Chapter 11 New Families of ECM Curves for Cunningham Numbers
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    Chapter 12 Visualizing Elements of Sha[3] in Genus 2 Jacobians
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    Chapter 13 On Weil Polynomials of K3 Surfaces
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    Chapter 14 Class Invariants by the CRT Method
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    Chapter 15 Short Bases of Lattices over Number Fields
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    Chapter 16 On the Complexity of the Montes Ideal Factorization Algorithm
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    Chapter 17 Congruent Number Theta Coefficients to 1012
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    Chapter 18 Pairing the Volcano
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    Chapter 19 A Subexponential Algorithm for Evaluating Large Degree Isogenies
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    Chapter 20 Huff’s Model for Elliptic Curves
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    Chapter 21 Efficient Pairing Computation with Theta Functions
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    Chapter 22 Small-Span Characteristic Polynomials of Integer Symmetric Matrices
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    Chapter 23 Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field
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    Chapter 24 Factoring Polynomials over Local Fields II
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    Chapter 25 On a Problem of Hajdu and Tengely
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    Chapter 26 Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures
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    Chapter 27 On the Extremality of an 80-Dimensional Lattice
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    Chapter 28 Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number
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    Chapter 29 Improved Primality Proving with Eisenstein Pseudocubes
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    Chapter 30 Hyperbolic Tessellations Associated to Bianchi Groups
Attention for Chapter 26: Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures
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Chapter title
Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures
Chapter number 26
Book title
Algorithmic Number Theory
Published by
Springer, Berlin, Heidelberg, July 2010
DOI 10.1007/978-3-642-14518-6_26
Book ISBNs
978-3-64-214517-9, 978-3-64-214518-6
Authors

Jonathan P. Sorenson