Algorithmic Number Theory
Springer Berlin (Verlag)
978-3-540-36075-9 (ISBN)
Invited Talks.- Computing Pro-P Galois Groups.- The Elliptic Curve Database for Conductors to 130000.- On the Computation of the Coefficients of a Modular Form.- Cohen-Lenstra Heuristics of Quadratic Number Fields.- Algebraic Number Theory.- An Algorithm for Computing p-Class Groups of Abelian Number Fields.- Computation of Locally Free Class Groups.- Numerical Results on Class Groups of Imaginary Quadratic Fields.- Cyclic Polynomials Arising from Kummer Theory of Norm Algebraic Tori.- The Totally Real Primitive Number Fields of Discriminant at Most 109.- A Modular Method for Computing the Splitting Field of a Polynomial.- Analytic and Elementary Number Theory.- On the Density of Sums of Three Cubes.- The Mertens Conjecture Revisited.- Fast Bounds on the Distribution of Smooth Numbers.- Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables.- The Pseudosquares Prime Sieve.- Doubly-Focused Enumeration of Pseudosquares and Pseudocubes.- Lattices.- Practical Lattice Basis Sampling Reduction.- LLL on the Average.- On the Randomness of Bits Generated by Sufficiently Smooth Functions.- Curves and Varieties over Fields of Characteristic Zero.- Computing a Lower Bound for the Canonical Height on Elliptic Curves over ?.- Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over with Small d.- Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group, and Some Other Examples.- The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds.- Testing Equivalence of Ternary Cubics.- Classification of Genus 3 Curves in Special Strata of the Moduli Space.- Heegner Point Computations Via Numerical p-Adic Integration.- Symmetric Powers of Elliptic Curve L-Functions.-Determined Sequences, Continued Fractions, and Hyperelliptic Curves.- Computing CM Points on Shimura Curves Arising from Cocompact Arithmetic Triangle Groups.- Arithmetic of Generalized Jacobians.- Hidden Pairings and Trapdoor DDH Groups.- Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10.- Fast Bilinear Maps from the Tate-Lichtenbaum Pairing on Hyperelliptic Curves.- High Security Pairing-Based Cryptography Revisited.- Efficiently Computable Endomorphisms for Hyperelliptic Curves.- Construction of Rational Points on Elliptic Curves over Finite Fields.- 20 Years of ECM.- Discrete Logarithms.- An Index Calculus Algorithm for Plane Curves of Small Degree.- Signature Calculus and Discrete Logarithm Problems.- Spectral Analysis of Pollard Rho Collisions.- Hard Instances of the Constrained Discrete Logarithm Problem.
| Erscheint lt. Verlag | 6.7.2006 |
|---|---|
| Reihe/Serie | Lecture Notes in Computer Science |
| Zusatzinfo | XII, 599 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 853 g |
| Themenwelt | Mathematik / Informatik ► Informatik |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Algebraic Geometry • Algebraic Number Fields • algebraic number theory • algorithm • Algorithm analysis and problem complexity • Algorithmic Number Theory • algorithms • Calculus • Computational Number Theory • cryptography • Database • Elliptic Curve Computations • Factoring • finite field • Finite Field Computations • Galois groups • Lattice Computations • L-functions • modular form • number-theoretic algorithms • Number Theory • Prime • Variable • Zeta functions |
| ISBN-10 | 3-540-36075-1 / 3540360751 |
| ISBN-13 | 978-3-540-36075-9 / 9783540360759 |
| Zustand | Neuware |
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