Algorithmic Number Theory

Table of Contents

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   Book Overview
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   Chapter 1 Computing Zeta Functions via p -Adic Cohomology
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   Chapter 2 Using Primitive Subgroups to Do More with Fewer Bits
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   Chapter 3 Elliptic Curves of Large Rank and Small Conductor
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   Chapter 4 Binary GCD Like Algorithms for Some Complex Quadratic Rings
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   Chapter 5 On the Complexity of Computing Units in a Number Field
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   Chapter 6 Implementing the Arithmetic of C 3,4 Curves
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   Chapter 7 Pseudocubes and Primality Testing
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   Chapter 8 Elliptic Curves with a Given Number of Points
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    Chapter 9 Rational Divisors in Rational Divisor Classes
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    Chapter 10 Conjectures about Discriminants of Hecke Algebras of Prime Level
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    Chapter 11 Montgomery Scalar Multiplication for Genus 2 Curves
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    Chapter 12 Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves
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    Chapter 13 Elliptic Curves x 3 + y 3 = k of High Rank
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    Chapter 14 Proving the Primality of Very Large Numbers with fastECPP
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    Chapter 15 A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii’s Algorithm
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    Chapter 16 Function Field Sieve in Characteristic Three
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    Chapter 17 A Comparison of CEILIDH and XTR
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    Chapter 18 Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication
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    Chapter 19 An Algorithm for Computing Isomorphisms of Algebraic Function Fields
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    Chapter 20 A Method to Solve Cyclotomic Norm Equations $f * \bar{f}$
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    Chapter 21 Imaginary Cyclic Quartic Fields with Large Minus Class Numbers
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    Chapter 22 Nonic 3-adic Fields
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    Chapter 23 Montgomery Addition for Genus Two Curves
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    Chapter 24 Numerical Evaluation at Negative Integers of the Dedekind Zeta Functions of Totally Real Cubic Number Fields
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    Chapter 25 Salem Numbers of Trace -2 and Traces of Totally Positive Algebraic Integers
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    Chapter 26 Low-Dimensional Lattice Basis Reduction Revisited
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    Chapter 27 Computing Order Statistics in the Farey Sequence
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    Chapter 28 The Discrete Logarithm in Logarithmic l -Class Groups and Its Applications in K-theory
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    Chapter 29 Point Counting on Genus 3 Non Hyperelliptic Curves
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    Chapter 30 Algorithmic Aspects of Cubic Function Fields
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    Chapter 31 A Binary Recursive Gcd Algorithm
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    Chapter 32 Lagrange Resolvents Constructed from Stark Units
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    Chapter 33 Cryptanalysis of a Divisor Class Group Based Public-Key Cryptosystem