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Algorithmic Number Theory [electronic resource] : 9th International Symposium, ANTS-IX, Nancy, France, July 19-23, 2010, Proceedings / edited by Guillaume Hanrot, Francois Morain, Emmanuel Thomé.

Contributor(s): Hanrot, Guillaume [editor.] | Morain, Francois [editor.] | Thomé, Emmanuel [editor.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Theoretical Computer Science and General Issues: 6197Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2010Edition: 1st ed. 2010.Description: XI, 397 p. 15 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783642145186.Subject(s): Algorithms | Computer science -- Mathematics | Discrete mathematics | Cryptography | Data encryption (Computer science) | Number theory | Algorithms | Discrete Mathematics in Computer Science | Cryptology | Symbolic and Algebraic Manipulation | Number TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 518.1 Online resources: Click here to access online
Contents:
Invited papers -- Putting the Hodge and Tate Conjectures to the Test -- Curves of Genus 3 with a Group of Automorphisms Isomorphic to S3 -- Learning with Errors over Rings -- Lattices and Spherical Designs -- Fixed Points for Discrete Logarithms -- Contributed papers -- Explicit Coleman Integration for Hyperelliptic Curves -- Smallest Reduction Matrix of Binary Quadratic Forms -- Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields -- On the Use of the Negation Map in the Pollard Rho Method -- An O(M(n) logn) Algorithm for the Jacobi Symbol -- New Families of ECM Curves for Cunningham Numbers -- Visualizing Elements of Sha[3] in Genus 2 Jacobians -- On Weil Polynomials of K3 Surfaces -- Class Invariants by the CRT Method -- Short Bases of Lattices over Number Fields -- On the Complexity of the Montes Ideal Factorization Algorithm -- Congruent Number Theta Coefficients to 1012 -- Pairing the Volcano -- A Subexponential Algorithm for Evaluating Large Degree Isogenies -- Huff's Model for Elliptic Curves -- Efficient Pairing Computation with Theta Functions -- Small-Span Characteristic Polynomials of Integer Symmetric Matrices -- Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field -- Factoring Polynomials over Local Fields II -- On a Problem of Hajdu and Tengely -- Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures -- On the Extremality of an 80-Dimensional Lattice -- Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number -- Improved Primality Proving with Eisenstein Pseudocubes -- Hyperbolic Tessellations Associated to Bianchi Groups.
In: Springer Nature eBook
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Invited papers -- Putting the Hodge and Tate Conjectures to the Test -- Curves of Genus 3 with a Group of Automorphisms Isomorphic to S3 -- Learning with Errors over Rings -- Lattices and Spherical Designs -- Fixed Points for Discrete Logarithms -- Contributed papers -- Explicit Coleman Integration for Hyperelliptic Curves -- Smallest Reduction Matrix of Binary Quadratic Forms -- Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields -- On the Use of the Negation Map in the Pollard Rho Method -- An O(M(n) logn) Algorithm for the Jacobi Symbol -- New Families of ECM Curves for Cunningham Numbers -- Visualizing Elements of Sha[3] in Genus 2 Jacobians -- On Weil Polynomials of K3 Surfaces -- Class Invariants by the CRT Method -- Short Bases of Lattices over Number Fields -- On the Complexity of the Montes Ideal Factorization Algorithm -- Congruent Number Theta Coefficients to 1012 -- Pairing the Volcano -- A Subexponential Algorithm for Evaluating Large Degree Isogenies -- Huff's Model for Elliptic Curves -- Efficient Pairing Computation with Theta Functions -- Small-Span Characteristic Polynomials of Integer Symmetric Matrices -- Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field -- Factoring Polynomials over Local Fields II -- On a Problem of Hajdu and Tengely -- Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures -- On the Extremality of an 80-Dimensional Lattice -- Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number -- Improved Primality Proving with Eisenstein Pseudocubes -- Hyperbolic Tessellations Associated to Bianchi Groups.

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