The Resource Algebraic curves and cryptography, V. Kumar Murty, editor

Algebraic curves and cryptography, V. Kumar Murty, editor

Label
Algebraic curves and cryptography
Title
Algebraic curves and cryptography
Statement of responsibility
V. Kumar Murty, editor
Contributor
Subject
Language
eng
Member of
Cataloging source
DLC
Dewey number
516.3/52
Index
index present
LC call number
QA565
LC item number
.A44 2010
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1956-
http://library.link/vocab/relatedWorkOrContributorName
Murty, Vijaya Kumar
Series statement
Fields Institute communications
Series volume
58
http://library.link/vocab/subjectName
  • Curves, Algebraic
  • Commutative rings
  • Coding theory
  • Cryptography
Label
Algebraic curves and cryptography, V. Kumar Murty, editor
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • 1.3.
  • The Diffie-Hellman decision problem
  • 1.4.
  • Constraints on the group
  • 1.5.
  • Abelian varieties over finite fields
  • 1.6.
  • Elliptic curves
  • 1.7.
  • Statistical results
  • Machine generated contents note:
  • 1.8.
  • Abelian varieties of higher dimension
  • 1.9.
  • Outline of contents
  • ch. 2
  • Schoof's Point Counting Algorithm
  • Nicolas Theriault
  • 2.1.
  • Preliminaries
  • 2.2.
  • ch. 1
  • Division polynomials
  • 2.3.
  • Schoof's algorithm
  • 2.4.
  • Implementation
  • 2.5.
  • Improvements by Atkin and Elkies
  • 2.6.
  • Computing the modular equations
  • 2.7.
  • An Overview of Algebraic Curves and Cryptography
  • Computing p1, a and b
  • 2.8.
  • Computing the factor of f1
  • 2.9.
  • Parallelization
  • ch. 3
  • Report on the Denef-Vercauteren/Kedlaya Algorithm
  • Pramathanath Sastry
  • 3.1.
  • Background
  • V. Kumar Murty
  • 3.2.
  • Generalities
  • 3.3.
  • Main strategy
  • 1.1.
  • Introduction
  • 1.2.
  • The basic paradigm
  • 3.8.
  • Inversion
  • 3.9.
  • The 2-power Frobenius on K
  • 3.10.
  • The characteristic polynomial of Frobenius
  • 3.11.
  • Multiplication
  • 3.12.
  • Running times
  • 3.4.
  • 3.13.
  • Parallelization
  • ch. 4
  • An Introduction to Grobner Bases
  • Mohammed Radi-Benjelloun
  • 4.1.
  • Introduction
  • 4.2.
  • Grobner bases
  • ch. 5
  • Monsky-Washnitzer cohomology
  • Cab Curves and Arithmetic on Their Jacobians
  • Farzali Izadi
  • 5.1.
  • Introduction
  • 5.2.
  • Preliminaries
  • 5.3.
  • The Cab curves
  • 5.4.
  • Addition algorithm for Jacobian group in divisor representation
  • 3.5.
  • 5.5.
  • Addition algorithm for Jacobian group in ideal representation
  • ch. 6
  • The Zeta Functions of Two Garcia-Stichtenoth Towers
  • Kenneth W. Shum
  • 6.1.
  • Introduction
  • 6.2.
  • Background on zeta functions
  • 6.3.
  • Hyperelliptic curves
  • The first Garcia-Stichtenoth tower
  • 6.4.
  • The second Garcia-Stichtenoth tower
  • 6.5.
  • Conclusion
  • 3.6.
  • Data structures
  • 3.7.
  • Algorithm for lifting the curve to characteristic zero
Dimensions
27 cm.
Extent
iv, 133 p.
Isbn
9780821843116
Isbn Type
(alk. paper)
Lccn
2010035455
System control number
  • (CaMWU)u2512368-01umb_inst
  • 2510722
  • (Sirsi) i9780821843116
  • (OCoLC)660087877
Label
Algebraic curves and cryptography, V. Kumar Murty, editor
Publication
Bibliography note
Includes bibliographical references and index
Contents
  • 1.3.
  • The Diffie-Hellman decision problem
  • 1.4.
  • Constraints on the group
  • 1.5.
  • Abelian varieties over finite fields
  • 1.6.
  • Elliptic curves
  • 1.7.
  • Statistical results
  • Machine generated contents note:
  • 1.8.
  • Abelian varieties of higher dimension
  • 1.9.
  • Outline of contents
  • ch. 2
  • Schoof's Point Counting Algorithm
  • Nicolas Theriault
  • 2.1.
  • Preliminaries
  • 2.2.
  • ch. 1
  • Division polynomials
  • 2.3.
  • Schoof's algorithm
  • 2.4.
  • Implementation
  • 2.5.
  • Improvements by Atkin and Elkies
  • 2.6.
  • Computing the modular equations
  • 2.7.
  • An Overview of Algebraic Curves and Cryptography
  • Computing p1, a and b
  • 2.8.
  • Computing the factor of f1
  • 2.9.
  • Parallelization
  • ch. 3
  • Report on the Denef-Vercauteren/Kedlaya Algorithm
  • Pramathanath Sastry
  • 3.1.
  • Background
  • V. Kumar Murty
  • 3.2.
  • Generalities
  • 3.3.
  • Main strategy
  • 1.1.
  • Introduction
  • 1.2.
  • The basic paradigm
  • 3.8.
  • Inversion
  • 3.9.
  • The 2-power Frobenius on K
  • 3.10.
  • The characteristic polynomial of Frobenius
  • 3.11.
  • Multiplication
  • 3.12.
  • Running times
  • 3.4.
  • 3.13.
  • Parallelization
  • ch. 4
  • An Introduction to Grobner Bases
  • Mohammed Radi-Benjelloun
  • 4.1.
  • Introduction
  • 4.2.
  • Grobner bases
  • ch. 5
  • Monsky-Washnitzer cohomology
  • Cab Curves and Arithmetic on Their Jacobians
  • Farzali Izadi
  • 5.1.
  • Introduction
  • 5.2.
  • Preliminaries
  • 5.3.
  • The Cab curves
  • 5.4.
  • Addition algorithm for Jacobian group in divisor representation
  • 3.5.
  • 5.5.
  • Addition algorithm for Jacobian group in ideal representation
  • ch. 6
  • The Zeta Functions of Two Garcia-Stichtenoth Towers
  • Kenneth W. Shum
  • 6.1.
  • Introduction
  • 6.2.
  • Background on zeta functions
  • 6.3.
  • Hyperelliptic curves
  • The first Garcia-Stichtenoth tower
  • 6.4.
  • The second Garcia-Stichtenoth tower
  • 6.5.
  • Conclusion
  • 3.6.
  • Data structures
  • 3.7.
  • Algorithm for lifting the curve to characteristic zero
Dimensions
27 cm.
Extent
iv, 133 p.
Isbn
9780821843116
Isbn Type
(alk. paper)
Lccn
2010035455
System control number
  • (CaMWU)u2512368-01umb_inst
  • 2510722
  • (Sirsi) i9780821843116
  • (OCoLC)660087877

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